Problems of increased difficulty. Programming methods: exhaustive algorithms

1

When it comes to war, we remember Stalingrad, and when we remember Stalingrad, we remember Zhukov. This is him greatest commander XX century, was the creator of one of the most brilliant operations of the Second World War, and, perhaps, of all world history. Stalingrad is a confirmation of the indisputable truth: where Zhukov is, there is victory! Stalingrad is proof of Zhukov’s genius: he glanced at the map and immediately found a solution!

Let's shout three times "Hurray" to the genius, and then ask a question about the reliability of the information. Let's get to the roots. Let's establish how it became known that the Stalingrad strategic plan offensive operation suggested by Zhukov?

The source is easy to find: Zhukov himself said this. It was he who declared himself the author of the operation plan, although he admitted that there was also a co-author - A.M. Vasilevsky. It is described like this:

“On the afternoon of September 12, I flew to Moscow and four hours later I was in the Kremlin, where the Chief of the General Staff A.M. Vasilevsky was also summoned...

The Supreme Commander took out his map with the location of General Headquarters reserves and looked at it for a long time and intently. Alexander Mikhailovich and I moved away from the table to the side and talked very quietly about the fact that, apparently, we need to look for some other solution.

What is the “other” solution? - suddenly, raising his head, asked I.V. Stalin.

I never thought that I.V. Stalin had such a keen ear. We approached the table...

The whole next day A.M. and I Vasilevsky worked in General Staff... Having gone through everything possible options, we decided to propose to Stalin the following plan of action..." ("Memories and Reflections". M. APN. 1969. P.401-402)

From the above it follows that at the origins of the Stalingrad strategic offensive operation there were three people: Stalin, Zhukov and Vasilevsky. Stalin's merit is that his hearing is sharp. Stalin heard that Zhukov and Vasilevsky were whispering, became interested, and it was then that Zhukov and his comrade in arms gave the Supreme Commander-in-Chief a brilliant idea...

Zhukov said that Stalin doubted success, was afraid to take risks, and proposed carrying out an operation, but not on such a scale, but more modestly. But Zhukov persuaded Stalin, and everything turned out as it should.

2

Zhukov speaks in detail and at length about Stalingrad through the mouths of his literary blacks: “On July 12, the headquarters created a new Stalingrad front...” “By the end of July, the Stalingrad Front included..." "A lot of organizational work was carried out by the regional committee and city party committee of Stalingrad on the formation and preparation of the people's militia..."

All this is true, all this is interesting, but let us pay attention to a small detail: in July 1942, Zhukov was not in Stalingrad and could not have been. He was in a completely different direction, very far from Stalingrad. Everyone who is interested in the war has the opportunity to restore the chronology of Zhukov’s work at the front day by day, from the first to last day war. Sometimes - accurate to hours and minutes. From October 11, 1941 to August 26, 1942, Zhukov commanded the troops of the Western Front, which fought in a completely different direction, a thousand kilometers from Stalingrad. Until August 26, 1942, Zhukov could not and did not have the right to deal with the affairs of Stalingrad.

This is what happened at Stalingrad. In the spring of 1942, the Soviet Southwestern Front collapsed. The culprits of the disaster are Timoshenko, Khrushchev and Bagramyan. But the main culprit is Zhukov. Because of his lies, because of his victorious reports about grandiose victories in the main direction of the war, Stalin squandered strategic reserves and at a critical moment was not able to close the gap that had formed. German troops rushed into the breakthrough. A popular uprising broke out in the rear of the Red Army. The population of the Don, Kuban, North Caucasus, Kalmyk steppes. The Red Army found itself in the position of an occupier on its own land, the ground was burning under its feet. The rebels hanged security officers, communists and commissars, crushed their heads, and drowned them in rivers and swamps. Soviet regiments and divisions scattered, troops scattered. Meanwhile, the flow of German troops was divided in two. One direction of attack is towards Grozny and Baku. The intention is to reach sources of oil. The second direction is to Stalingrad. The intention is to protect the troops rushing to the Caucasus from possible strike into the flank and cut the Volga - the oil aorta Soviet Union. The critical situation at Stalingrad developed in July 1942. The exit of German troops to the Volga at that moment inevitably led to the collapse of the entire southern wing of the Soviet-German front with catastrophic consequences for the country's economy.

By personal order of Stalin, a new Stalingrad Front was created, which included four combined arms and one air army from the collapsed Southwestern Front. In addition, from his strategic reserve, Stalin moved the 62nd, 63rd and 64th armies to the Stalingrad area. On July 28, Stalin single-handedly signed the draconian order No. 227 “Not a step back!” Stalin personally took full responsibility for the situation at Stalingrad and for any measures that could stop the flight Soviet troops. On July 30, by order of Stalin, the 51st Army was included in the Stalingrad Front. On August 9, Stalin threw the 1st Guards Army at Stalingrad. At the head of this army, Stalin put former boss GRU, his future deputy Lieutenant General F.I. Golikova. The 1st Guards Army was equipped with the best human material. Five airborne corps were sent to form it, which were turned into guards rifle divisions. In mid-August, Stalin sent the 24th and 66th armies to the Stalingrad area. Troops marched towards Stalingrad in a continuous stream. Dozens of penal battalions and companies were sent here. At Stalingrad, Stalin abandoned nineteen military schools, including Zhitomir, Vinitskoe, Grozny, 1st and 2nd Ordzhonikidze Infantry Schools, Krasnodar Machine Gun and Mortar School, Chelyabinsk, Stalingrad, Omsk, Kazan Tank. And in each of these schools there were “from 3.5 to 5 thousand of the best Red Army soldiers and sergeants aged 18-22 years old, selected from advanced positions with experience in participating in battles.” (A.M. Samsonov “Know and Remember.” Moscow IPL. 1989. P. 136) Stalin sent the 5th, 7th, 8th and 10th sapper armies to build defensive structures near Stalingrad. I know what an engineer company and an engineer battalion are. I saw with my own eyes the engineer regiment in in full force and in all its glory. I didn’t have the chance to see the entire sapper brigade, but I can clearly imagine it. But I can’t imagine a sapper division. It doesn't work. There are too many sappers. Moreover, I can’t imagine a corps that consists of only sappers. But Stalin is not talking about sapper brigades, divisions and corps. Stalin had entire sapper armies in reserve. The Soviet Union is the only country in the world that had sapper armies. Stalin sent four such armies at once to build defensive lines near Stalingrad. In addition to these sapper armies, Stalin moved several defensive construction departments of the RVGK from his personal reserve to Stalingrad to create a strategic defensive belt. What they were can be judged from one example. Only the personnel of the 24th Defense Construction Directorate from Stalin’s personal reserve dug 1,448 kilometers of trenches and trenches, 57 kilometers of anti-tank ditches, 51 kilometers of scarps, 8 kilometers of gouges and 24,400 firing points in the Stalingrad area. Firing points were created not only from wood and earth, but from reinforced concrete and steel. The personnel of the 24th Defense Construction Directorate of the RVGK alone assembled 1,112 tons of metal structures and 2,317 cubic meters of reinforced concrete structures. ("Red Star" January 10, 1985) To the work of the 24th defensive construction department of the RVGK we will add the work of other defensive construction departments and the work of four sapper armies. Imagine the scale of defensive work in this area, we can only be amazed at the tenacity of Hitler and his generals, who threw their divisions into suicidal attacks on such defenses.

In addition to the artillery, which consisted of ten combined arms and one Guards Army, Stalin from his personal reserve nominated 129 artillery regiments of the RVGK and 115 separate divisions to Stalingrad rocket artillery. One can endlessly list fighter, assault and bomber aviation regiments, divisions and corps, reserve aviation groups, tank and mechanized brigades and corps, mortar divisions and regiments, communications units and units, repair, medical and other formations that Stalin threw into the battle on the Volga . In July and August 1942, all these regiments, brigades, divisions, corps and armies were either already in the Stalingrad area, or were being transferred to the Stalingrad area, or were preparing to be transferred. I'm not talking about the 2nd Guards and 5th Tank Armies, the four tank and two mechanized corps, which in the summer of 1942 were formed deep in the rear and prepared for winter battles. In any case, we cannot escape the recognition: many troops were sent to Stalingrad. All this was done while Zhukov was on another, namely, the Western Front. In July and August 1942, the main thing was done without Zhukov - panic in the troops was suppressed by draconian measures, fleeing troops were stopped, a new Soviet front was created in the area of ​​​​the strategic breakthrough of German troops, an insurmountable defense was erected, fresh divisions, corps and armies were brought up. In the summer of 1942, the enemy’s actions were transformed from rapid, unstoppable movement into protracted battles for every line, every trench and every firing point, which was extremely disadvantageous for him. And winter is ahead. In any case, in the summer of 1942, conditions were created in the Stalingrad area that inevitably led the German army to disaster. So many forces were gathered at Stalingrad that military genius was not required.

3

And so we open Zhukov’s book and read about how in the summer of 1942 the enemy rushed to Stalingrad, how the Red Army heroically fought the enemy, how it stopped the enemy offensive. Zhukov vividly recalls and colorfully talks about events to which he had nothing to do. If we are interested in the situation in July 1942 near Stalingrad, we will find enough sources. The book “Memories and Reflections” was written on behalf of Zhukov, so it would be correct to talk not about the Stalingrad Front, where Zhukov was not, but about the Western Front, which Zhukov commanded at that moment. But everything that happened in the spring and summer of 1942 on the Western Front is described in the memoirs in one paragraph. The authors of Zhukov’s memoirs were carried to strategic heights: “The 37th and 12th armies of the North Caucasus Front received the task...” Why are they telling us about the Caucasus if Zhukov was not there? But they don’t let up: “At the call of the Central Committee of the Party of Georgia, Azerbaijan and Armenia, armed detachments were formed...”

Zhukov's memoirs describe in detail the 1942 disaster in the Kharkov region. And the culprits were named. But Zhukov was not there either. Zhukov was not responsible for this direction. The disaster of the Crimean Front is described. And again the culprits are named. But Zhukov didn’t fight in Crimea either; Crimea is not his concern. Zhukov's memoirs describe the defeat of Soviet troops near Voronezh, the authors recalled the fall of Sevastopol and unsuccessful attempt troops of the Northwestern Front to liquidate the German group in the Demyansk area. Zhukov did not take part in all these events. Why is all this included in the memoirs?

Firstly, they demonstrated the strategic breadth of Zhukov’s horizons.

Secondly, they showed the harsh bitter truth: look at the defeats... of Zhukov’s neighbors, look at the miscalculations of stupid Stalin and the commanders of all fronts where Zhukov is not present.

Thirdly, they filled the chapter about 1942 with extraneous descriptions so that there was no room left for the story about Zhukov himself and his deeds.

Meanwhile, 1942 for the Western Front, commanded by Zhukov, was a year of severe defeats and huge losses. On the Western Front, Zhukov carried out continuous stupid offensive operations, each of which ended in failure. The bloodiest of them: Rzhevsko-Sychevskaya - July 30 - August 23.

It is interesting that the “Soviet Military Encyclopedia” (Vol. 7, pp. 119-120) clearly defines the timing of this operation, lists the armies and corps that were involved in carrying it out, and includes a map. If an encyclopedia describes an operation, then it deserves it. But Zhukov, who carried out this operation, does not report the timing of the operation, nor the forces that were involved, and does not include a map. Instead, from Zhukov’s memoirs we learn:

• about the insidious policies of the USA and Great Britain;
• about Stalin's plans for 1942;
• about Hitler's plans for 1942;
• about party-political work in the Red Army;
• about the exploits of ordinary soldiers and sergeants;
• about the resistance of the Soviet people behind enemy lines;
• about the heroic work of workers and peasants;
• about the leadership and guiding role Communist Party and its wise Central Committee;
• about operations on all fronts except the Western.

In Zhukov’s memoirs there is no map of the Rzhev-Sychevsky operation, which Zhukov carried out, but there is another map: this is how the Germans rushed to Stalingrad, in which Zhukov was not at that time, for the defense of which Zhukov was not responsible at that moment.

And we are not interested in Stalingrad, but in Zhukov and the Rzhev-Sychevsk operation, about which he modestly keeps silent. To carry out this operation, Zhukov concentrated the 20th and 31st Armies, the 1st Air Army, the 6th and 8th Tank Corps, and the 2nd Guards Cavalry Corps. Neither Zhukov nor the Soviet Military Encyclopedia report how many people, tanks, guns, aircraft there were in these armies and corps. But we ourselves see that the forces are considerable. Zhukov's memoirs say that the Germans suffered at Sychevka " big losses"The sources are silent about our losses. Apparently, there were no losses.

To help Zhukov, troops from the left wing of the Kalinin Front struck in the direction of the same Sychevka: the 29th and 30th armies with the support of the 3rd Air Army.

Four combined arms armies, a cavalry corps, two separate tank corps supported by two air armies... for the assault on Sychevka!?

Isn't that a lot?

No, no. This was not enough for Zhukov.

Did the brilliant Zhukov take that same Sychevka with such forces? Alas.

What is the reason for the failure? Who's to blame? The reason is that they didn’t put enough effort into Sychevka. In total, Zhukov had only ten armies on the Western Front at that moment. He still lacked “one or two armies.” It is clear that Stalin is to blame for not giving these armies to Zhukov. “If we had one or two armies at our disposal, it would be possible... Unfortunately, this real opportunity was missed by the Supreme Command.” ("Memories and Reflections" Page 395)

But this assault on Sychevka is not the first. From January to August 1942, five armies of Konev and ten armies of Zhukov rushed to Rzhev and Sychevka. Let me remind you again: Zhukov was not only the commander of the Western Front, but also the commander-in-chief of the Western direction, which included the Western Front (Zhukov) and the Kalinin Front (Konev). In other words, Konev’s five armies were also subordinate to Zhukov. Before the next Rzhev-Sychevsk operation, the Supreme Command Headquarters on August 5, 1942 once again confirmed Zhukov’s powers: he led not only the operations of his Western Front, but also the neighboring Kalinin Front. (VIZH 1991, No. 10. P. 24)

In the area of ​​Rzhev and Sychevka, corpses were already lying in layers Soviet soldiers, killed in previous assaults. Entire cemeteries of burnt-out Soviet tanks were already piled up there. All the front-line soldiers remembered the months-long stupid meat grinder near Rzhev and Sychevka under the leadership of the brilliant Zhukov. One of the most poignant poems about the war was written by Alexander Tvardovsky. And it’s not for nothing that it’s called “I was killed near Rzhev.” Let's remember:

The front was burning without subside,
Like a scar on the body.
I'm killed and I don't know:
Is Rzhev finally ours?

Storm. Storm. Storm. To the forehead. Same pattern as yesterday. According to the same program. Five attacks a day. Seven each. Ten each. To the same high-rise buildings. Month after month. From January to August. Forward! Zhukov is with us!

4

Our official historians have invented a special language and a whole series of special techniques with which they hide failures in the war, primarily Zhukov’s failures. However, there are quite reliable indicators of lies. Here's one of them. Let's say you come across a description of an offensive operation, but the code name of this operation is not reported. Know that this is a lie.

The point here is this. Most defensive operations do not have code names. The enemy strives to do what we do not expect, what we are not ready for, what our plans do not provide for. The enemy is trying to strike where we planned defensive actions on a much smaller scale or did not plan them at all. Therefore, in many cases, a defensive operation is an improvisation. In addition, in a defensive operation there is no need to hide our intentions. If we defend Stalingrad, therefore, we intend to hold it.

And we are preparing the offensive operation ourselves. We must hide from the enemy the time, place, purpose, intention, composition of forces and much more. Therefore, the preparation of an offensive operation begins with assigning a code name to it. This is done to maintain secrecy. There is a conversation going on at the General Staff about "Little Saturn", if you are privy to the secret, you understand what we are talking about. If you are not entrusted with the secret, then you will not understand anything. "Uranus", "Anadyr", "S.3-20", "Thunderstorm", "Bagration". What is this? What are the generals talking about? If you know, everything is simple. If you don't know, it's a dead end. Even a cryptographer, admitted to many great secrets, has no idea what the essence of the message being transmitted is. He writes: “Iskra”, but does not know what is hidden behind this name.

Half a century has passed since the war, and in a very thick encyclopedia we find descriptions of offensive operations with strange names: Rzhevsko-Sychevskaya, Rzhevsko-Vyazemskaya, Sychevsko-Vyazemskaya. The code names of these operations are not reported. And we’ll figure it out: could Zhukov, at the headquarters of the Western Front, plan an operation and call it Rzhevsko-Sychevskaya or Sychevsko-Vyazemskaya? No, I couldn't. If he called the operation that way, then by the very name of the operation he gave away his intentions and his plan to all the staff typists and telephone operators, all the draftsmen, clerks and security guards. If Zhukov is not a complete idiot, it means that he used code names when preparing these operations. Why aren’t they telling us after half a century?

Because these operations are still, after 50 and 60 years, still classified. The reason for secrecy is this. It was planned, for example, to defeat the German Army Group Center with a breakthrough 600 kilometers deep and the exit of Soviet troops to the coast Baltic Sea. But the group of German armies was not defeated, they did not break through the defenses, they advanced not 600 kilometers, but 23. They planned to reach Vitebsk, Minsk and Riga, but they only reached Sychevka, and could not take it.

How to cover up the embarrassment? State secret. In this case, our military-historical oligarchs classify the entire operation as secret. The code name, goals, objectives and design of the operation, the composition of the forces and assets involved, and most importantly, losses, fall into the category of state secrets. Instead of all this, our academics write in the encyclopedia: yes, there were battles in this area, but nothing serious was planned, planned or conceived here. They just wanted to capture Rzhev, which is 6 kilometers from the front line, and Sychevka, which is already 50 kilometers away. True, neither Rzhev nor Sychevka were taken either the first time, or the third, or the thirteenth, or the forty-first.

Let’s think about this: could Stalin give Zhukov combat mission capture some Sychevka? Isn't it too small for Stalin? And for Zhukov? And for the Western Front, which is assisted by the Kalinin Front?

On August 23, 1942, the next attack on Sychevka failed, and on August 26, Stalin appointed Zhukov as his deputy.

Let us note: not after great victories, the commander of the Western Front, Zhukov, was promoted and became Deputy Supreme Commander-in-Chief, but after eight months of bloody, hopeless meat grinder. It is not for brilliant victories that Stalin raises Zhukov, not for brilliant thoughts. Stalin liked Zhukov for other qualities: he drove hundreds of thousands of people to death for many months and did not even flinch his face!

Stalin needed to have two people with completely different characteristics as assistants. It’s like a regiment commander: the chief of staff is a thinker, and the deputy regiment commander is a go-getter. The regiment commander is responsible for everything. The chief of staff is nearby. He is a generator of ideas. He is the Control Mechanism. And where it is decided in at the moment the most important task, the commander sends his deputy there to yell and swear.

At all other levels, the system is the same: any boss should always have one assistant, so to speak, in the thinking part, and another in the punching part. Stalin did the same at the very top. Under Stalin - the thinker Vasilevsky. He makes plans. But we also need someone whose job is to drive people to death. And this is work for Zhukov. Zhukov is the eldest, where they will send him. This is the deputy on the firing line, the assistant to the Supreme Commander-in-Chief for the massacre.

5

Zhukov first arrived in Stalingrad on August 31, 1942. He tried to launch counterattacks on the German troops that had broken through. Nothing came of this venture. The counterattacks ended in failure. By the way, a hint of failure is also contained in Zhukov’s memoirs. He visited Stalingrad, did something there for almost two weeks, and returned to Moscow on September 12. And then in Stalin’s office the same scene takes place, which Zhukov has repeatedly described with gusto: he whispered with Vasilevsky that it was necessary to look for some other solution. Stalin heard and became interested: what is the solution?

Zhukov said these words after he visited Stalingrad and tried to launch counterattacks there. Zhukov proposes to look for another solution because no sense came of the solution that Zhukov had already tried to implement at Stalingrad in the first days of September. Zhukov's actions turned out to be fruitless and useless.

There were several more trips by Zhukov to Stalingrad during the defensive battle. But Zhukov was not the only one who appeared there. Politburo member Georgy Malenkov, among others, visited Stalingrad. We do not declare Malenkov a strategist and savior for this. And we are not sculpting an equestrian statue of Malenkov. And we do not rank among the saints.

The last time Zhukov left the Stalingrad area was on November 16, 1942. And the counter-offensive of the Soviet troops began on November 19. Without Zhukov. Stalin again threw Zhukov into the Western direction. Again - against Sychevka!

On the day when the Stalingrad strategic offensive operation began, Zhukov was exactly one thousand kilometers from Stalingrad and was engaged in a completely different matter.

Chapter 16. AND AGAIN TO SYCHEVKA!

Arriving with the troops at the front, I was immediately able to grasp the situation, take control over the threads of control and turn events in the right direction.

1

The Stalingrad counteroffensive was conceived as a secondary operation. Anyone can find ample evidence of this in the memoirs of the participants in this operation. Marshals of the Soviet Union A.M. Vasilevsky, K.K. Rokossovsky, A.I. Eremenko, Chief Marshal of Artillery N.N. Voronov and others report that, having completed the encirclement of German troops at Stalingrad, Soviet commanders were surprised to find that there were three times more German divisions in the pocket than expected. The Soviet command intended to encircle 7-8 German divisions in the Stalingrad area, but there were 22 of them. In other words, the operation at Stalingrad was not planned to be as grandiose as it actually turned out. The result at Stalingrad was expected to be three times more modest. And the main operation was being prepared in the Western direction. Again, a breakthrough was planned at Rzhev, Sychevka and Vyazma in the direction of the Gulf of Riga. Zhukov is doing the same job again: coordinating the actions of the Kalinin and Western fronts. In addition, the offensive of the two fronts is supported by troops of the North-Western and Bryansk fronts.

To carry out this grandiose operation, greater forces were assembled than for the counteroffensive at Stalingrad. Under the command of Zhukov this time there were almost two million soldiers and officers, 3,300 tanks, more than a thousand combat aircraft, 24 thousand guns and mortars. The total combat weight of Soviet tanks involved in this operation was 2.8 times higher than the combat weight of all German tanks that Hitler threw at the Soviet Union on June 22, 1941.

And Zhukov failed this operation again in November-December 1942.

Where Zhukov was, there was a shameful defeat, rivers of blood, pyramids of soldiers' bones and almost two thousand burnt Soviet tanks. This is in addition to what was already put into the ground in the area from January to August. And at Stalingrad, where Zhukov was not there, there was victory.

2

Another failure of Zhukov at Sychevka, Rzhev and Vyazma has disappeared from our history. They forgot about him. And if any of the meticulous researchers are curious about where the great strategist Zhukov was at the time of the start of the Stalingrad strategic offensive operation, then the answer was prepared for such: Zhukov was in a secondary direction, there he carried out a diversionary operation.

During Brezhnev’s time, the entire ideological machine of the Soviet Union worked to inflate Zhukov’s personality cult. In those glorious times, Marshal Vasilevsky, who was already 82 years old and had a year left before his death, was forced to write: “On November 13... Zhukov was ordered to begin preparing a diversionary operation on the Kalinin and Western fronts, and I was entrusted with coordinating the actions of three fronts of the Stalingrad direction during the counter-offensive." ("VIZH" 1977 No11, p. 63)

Isn't that interesting? On November 19, 1942, a grandiose offensive operation begins near Stalingrad, which should turn the tide of the war in our favor, and a week before that, on November 13, the greatest commander of the twentieth century, Deputy Supreme Commander-in-Chief, Army General Zhukov, is given the task of conducting a diversionary operation in a completely different place! Surely, a diversionary operation cannot be entrusted to Konev, Govorov, Rokossovsky, Golikov, Tolbukhin, Bagramyan, Biryuzov, Voronov, Malinovsky or anyone else? Why did Stalin send Zhukov to the main direction in all operations, but during the Stalingrad strategic offensive operation he sent him to a secondary direction to carry out a diversionary operation?

The answer is simple: the operation near Sychevka, Rzhev and Vyazma in November-December 1942 was not a distraction, it was the main one. Zhukov failed it, so it was retroactively relegated to the category of secondary and distracting.

3

The operation in the Western strategic direction in November-December 1942 was not a diversionary operation, because a diversionary operation always precedes the main operation. First, the magician lulls our vigilance with something, and then takes it out of a black hat white rabbit. First, the pickpocket's henchmen show us someone else's wallet: weren't you the one who dropped it? And then the pickpocket himself, with a gentle movement, takes away our tight wallet. First, Odessa thief Benya Krik sets fire to a house opposite the police station, then, when the police rush to help the neighbors, he starts a fire in the police station. First the fighter makes a feint movement, then hits. It’s the same in war: first, a diversionary strike is launched in a secondary direction, then the main one in the main direction.

The counteroffensive at Stalingrad began on November 19, 1942, and the “diversionary” offensive of the Kalinin and Western fronts began on November 25, 1942. Let us ask: which of these operations should divert the enemy’s attention?

The operation of the Kalinin and Western fronts was not secondary and distracting, because more troops took part in it than in the offensive at Stalingrad. Zhukov, as part of the Kalinin and Western fronts, had 15 combined arms, 2 shock, 1 tank and 2 air armies. In addition, this “diversionary” offensive was facilitated by troops of the North-Western and Bryansk Fronts. These are 7 more combined arms, 1 shock and 2 air armies. In addition, behind this group there were one combined arms (68th) and two reserve (2nd and 3rd) armies. In total, Zhukov has 23 combined arms, 3 shock, 1 tank, 4 air and 2 reserve armies.

And Vasilevsky near Stalingrad has 10 combined arms, 1 tank and 3 air armies.

Which of these operations is the main one, which one is distracting?

The offensive of the Kalinin and Western fronts with the assistance of the Northwestern and Bryansk fronts in November-December 1942 was not distracting, and we learn this from the book of Zhukov himself. Here is the directive to the Kalinin and Western fronts issued on December 8, 1942. The immediate task of the Western Front: “During December 10-11, break through the enemy’s defenses in the Bolshaya Kropotovo - Yarygino sector and no later than December 15, capture Sychevka, December 20. withdraw at least two rifle divisions to the Andreevskoye area to organize the closure together with the 41st Army of the Kalinin Front of the encircled enemy." (Memories and reflections. pp. 435-436)

The Kalinin Front, among other things, was given the task of breaking through the front and “closing the encircled enemy group from the south together with units of the Western Front.” (Ibid.)

So, the Kalinin and Western fronts, led by Zhukov, were given the same task as the fronts at Stalingrad: to break through the enemy’s defenses in two sectors, break through with mobile formations deep into his rear and close the encirclement ring around the enemy group.

Let's believe communist propaganda. Let's assume that the Southwestern and Stalingrad fronts under the leadership of Vasilevsky in November 1942 broke through the enemy's defenses and closed the encirclement in order to turn the tide of the war in their favor. And in the same November, the Kalinin and Western fronts under the leadership of Zhukov were supposed to break through the enemy’s defenses and close the encirclement simply in order to divert Hitler’s attention.

And here is how the fronts led by Zhukov coped with their task. A word from Zhukov himself (or those who wrote his memoirs): “The command of the Kalinin Front, represented by Lieutenant General M.A. Purkaev, coped with its task. The group of front troops advancing south of the city of Bely, having successfully broken through the front, moved in the direction of Sychevka The group of troops of the Western Front, in turn, was supposed to break through the enemy’s defenses and move towards the troops of the Kalinin Front in order to close the encirclement around the Rzhev group of Germans. But it so happened that the Western Front did not break through the defenses... At this time. The situation on the Kalinin Front in the area of ​​our breakthrough became more complicated. With a strong blow the enemy cut off our flanks mechanized corps, commanded by Major General M.D. Solomatin, and the building remained surrounded." (Memories and Reflections. pp. 436-437)

Let's assume that all this was done for the sake of distraction. What is the result? The result is obvious. The troops led by Zhukov did not break through the German front, did not encircle the enemy, on the contrary, they themselves were surrounded. If you believe that this was simply a diversionary operation in a secondary direction, then we have to admit that at the moment when all the attention of Hitler and his field marshals was focused on Stalingrad, the troops under the leadership of Zhukov, even in the secondary direction, were unable to complete the task.

Several articles and books have already been written about Zhukov’s grandiose offensive in November-December 1942. To avoid being accused of malice, I will describe it not in my own words, but by quoting other authors. On June 8, 2001, the article “Not for battle, but for slaughter” appeared in the Independent Military Review. A story about the actions of the 20th Army of the Western Front alone in the next Rzhev-Sychevsk operation in November-December 1942. The authors of the article are M. Khodarenok and O. Vladimirov.

In this operation, the 20th Army of the Western Front, in addition to the forces it had, received reinforcements - two tank corps, eight separate tank brigades and a corresponding amount of artillery.

Subtitles of the article: “An unsuccessful start”, “The battle for the vegetable gardens of the village of Zherebtsovo”, “Stubbornness turning into madness”. This is said about the greatest strategist of the twentieth century.

Here are excerpts from the article:

“The troops on November 25 were actually sent not into battle, but to slaughter, under well-organized enemy fire.”

“Two rifle brigades of the 8th Guards Rifle Corps - the 148th and 150th - stormed the village of Khlepen, located on the high bank of the Vazuza, for four days... the 148th and 150th rifle brigades were killed almost in full force near the village, in of which there was no one left except the headquarters and support units."

“The inexorable Headquarters and its representative Georgy Zhukov demanded only one thing - an offensive at all costs. The 20th Army was further reinforced by the 5th Tank Corps and four rifle divisions.”

“The battlefield was littered with our burnt tanks. In particular, already on December 6, six of the eight tank brigades of the 20th Army, which had lost almost all their materiel, were withdrawn to the rear to restore combat capability.”

“Already on December 13, the 6th Tank Corps had 26 tanks in service, and two days ago the 5th Tank Corps, brought into battle, had only 30. One tank corps fought for the village of Maloe Kropotovo, the second tried to storm the village of Podosinovka.”

“During a week (December 11-18) of extremely bloody, fierce and essentially ineffective battles, the offensive capabilities of the 20th Army were completely exhausted. The ammunition and fuels and lubricants. The materiel of all eight tank brigades and both tank corps. The surviving people, who had been without sleep or food for several days, were extremely exhausted and mortally tired."

“For 23 days of continuous fighting, the troops of the 20th Army in an 8-kilometer sector bit into the enemy’s defenses for 10 kilometers. The average daily rate of attack was just over 400 meters per day. For each kilometer we had to pay with six thousand killed and wounded soldiers.”

“Events unfolded in approximately the same scenario in the offensive zones of other armies of the Western and Kalinin fronts.”

"The total human losses of the Kalinin and Western fronts amounted to more than 215 thousand people killed and wounded."

4

The 20th Army was not the only one to "distract". In the same way, all fifteen combined arms, two shock and one tank army The Western and Kalinin fronts, under the wise leadership of a brilliant commander, “distracted” Hitler’s attention. In addition, on other fronts, according to Zhukov’s scenario, seven more combined arms and one shock army were engaged in “distraction”.

Enough documents have been published about the actions of each army in this grandiose “diversionary” operation. It was not in vain that I chose the 20th Army. The 20th Army died in October 1941 near Yelnya. I won't say whose fault it is. Remember for yourself who stormed Yelnya for two months, bled the troops, wasted all the ammunition and fuel and lubricants and left for another front, exposing the exhausted and battered troops to defeat.

In November 1941, a new 20th Army was created. From the old 20th Army it inherited only its number. This new, poorly put together and untested association already in January 1942 under the command of Major General A.A. Vlasova worked miracles on the Lama River. And then Zhukov stood over Vlasov. And now a year has passed. The same 20th Army, the same Western Front. It's winter again. Now the 20th Army has already had a year combat experience. And again, general leadership is carried out by Zhukov. But now everything is not going as it should: reconnaissance is working poorly, artillery is firing not at targets but at areas, the entire preparation of the operation is clumsy. The enemy long ago realized where and what attacks would be delivered and did everything possible to repel them.

What is missing? General Vlasov is missing. Without him, Zhukov turned into an ordinary non-commissioned officer from the First World War.

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Problems of increased difficulty

(decisions, instructions, methodological advice)

Problems of increased difficulty are marked in the textbook with an or icon. Let's look at some of them. Before analyzing a problem of increased difficulty in class, you need to give it home so that students can think about it without limiting themselves with time. Then, as a class, review the solutions they come up with. If no one has solved it, or 1-3 people have solved it, the solution is not analyzed, but only a hint is given that will allow others to find ways of solving it. It’s better to give a hint in something like this: think about….

116 . How many different open broken lines can be constructed with vertices at points A, B, C, D(Fig. 16)?

Problem No. 000 is actually an enumeration problem. Her purpose in this section is to allow students to gain some experience in counting the number of options and constructing a tree of options before introducing the relevant terms and formulating the product rule.

After discussing the students' answers and solutions, the teacher might say something like the following:

“You received different answers, but no one could prove that he had too much All possible cases. Let's try to develop a way of counting in which we can be sure that we have gone through all possible options." Then the phrase “selection of... options” appears in such a context that its meaning does not need to be explained, especially since the words used by the students are already familiar to them from other life situations.

Next, students are asked to first calculate how many polygonal lines can be constructed starting at the point A. We reason like this: from the point A you can go to the point B or to the point C or to the point D. To make sure we don’t miss anything, let’s make a drawing:

Now let's think about where we can go from the point B, from point C, from point D, etc. As a result of the reasoning, we get the following picture:

“So, we see that we can build 6 broken lines starting at the point A. Let's write down their names. How many broken lines do you think we will get if we do the same work with the remaining points? Test your guess at home."

Here the work on the problem in class ends and students are asked to finish it at home: draw all the broken lines with a beginning at the point A and, reasoning similarly (having made the same drawing), write out and depict all broken lines with beginnings at points B, C And D. As students complete this activity, they will notice that each broken line is repeated twice because, for example, ABCD And DCBA– this is the same broken line. Therefore, the total number of different broken lines will not be 6 × 4 = 24, but half as many - 12.

The time spent working on a task in class can be reduced if you prepare in advance a slide with “trees” built from dots B, C And D.

117 . How many different closed broken lines can be constructed with vertices at points A, B, C, D(Fig. 16)?

Solution. The reasoning here could be as follows: “By going through possible options for open polylines, we initially received 24 options. Then we found out that we received 24 variants of the names of broken lines, and in these names each broken line is repeated twice, so there are 12 broken lines in total.

Let's turn open polylines into closed ones: add the necessary link. We see, for example, that closed broken lines ABCD, BCDA, CDAB And DABC- this is the same broken line,

i.e. the number of different closed broken lines is 4 times less number open: 12: 4 = 3.”

You can think differently. “Consider the closed broken line ABCD. Its name can be written in 8 ways (two names for each of the starting points A, B. C, D). This means that the number of closed broken lines is 8 times less than the number of all possible options for writing the names of broken lines with vertices at points A, B, C And D: 24: 8 = 3.”

And finally, the same result can be obtained by trying to draw various closed broken lines with vertices at these points. It is not possible to find more than three options.

161 . One day, in their spare time, Eeyore and Piglet decided to try to encrypt the numbers with letters. Eeyore managed to write down some three-digit number, then the sum of its digits, and then the sum of the digits of this sum. Here's what he got:

.

And Piglet did the same with another three-digit number. He got it like this:

Try to guess which number Eeyore wrote down and which number Piglet wrote down.

As a rule, there are students who cope with this task at home without any help. If there are only a few of them, there is no need to rush into telling everyone their decision. The answer to the question is enough: where did you start?

If there are no such students, a hint is given: think about what the sum of the digits of a three-digit number can be, can it start with the number 3, with the number 4, etc.? if not, why not? After this, the task is again assigned to the house.

Decision (one of the ways of reasoning).

1) I + O = I, which means O = 0. The sum of the digits of a three-digit number cannot be greater than + 9 + 9 = 27). Since O = 0, and I can only be equal to 2 or 1, the sum of the digits of the intended number is either 20 or 10. Let's check both options.

If I = 2, then IO = 20, then A must be equal to 16. But the number 16 does not exist.

If I = 1, then IO = 10, then A must be equal to 8. This is possible.

So Eeyore thought of the number 181.

2) Similarly for Piglet: the number of HO can be equal to 20 or 10, i.e. H can be equal to 2 or 1. Let's check these options.

If H = 2, then P = 9. This is possible.

If H = 1, then P cannot be determined, since P + P = 9, and 9 is not divisible by 2.

This means that Piglet came up with the number 929.

166 . A passerby noticed a bus going to the stop 180 meters behind him. In order not to be late, he ran and 12 seconds later he arrived at the stop at the same time as the bus. At what speed did the passerby have to run if it is known that the bus is moving at a speed of 19 m/sec?

Before giving this problem home, it is advisable to read it in class and make a drawing for it, that is, create a graphic model of the situation described in the problem:

1) 19 × 12 = 228 (m) – the distance traveled by the bus;

2) 228 – 180 = 48 (m) – the distance covered by the passerby;

3) 48: 12 = 4 (m/s) – speed of a passerby.

Answer: 4 m/s.

II method.

1) 180: 12 =15 (m/s) – the speed at which the bus catches up with a passerby;

2) 19 – 15 = 4 (m/s) – speed of a passerby.

Answer: 4 m/s.

Guiding questions to ask the class:

Which of the previously solved problems is this problem similar to? (problem No. 000, about the hat that the wind tore off the old woman Shapoklyak)

1) What quantity is required to be found in the problem? (speed)

2) What quantities do you need to know to determine the speed of movement? (path and time)

3) Which of them do we know? (time)

4) Think about how to define the path.

II method.

1) What movement? we're talking about in the problem: towards, after, do objects come closer or move away? How would you characterize the speed at which the relative position objects? (moving in pursuit, a bus catching up with a pedestrian, speed of approach)

2) In this problem, a bus and a passerby are moving, and the bus catches up with the passerby. What speeds and distances are considered when it comes to following? (the speed of moving objects, the speed of approaching or moving away, the distance between objects, the time it takes for one of them to catch up with the other).

4) Which of these quantities are known and which are not? Which one is the one you are looking for? (the time it took for the bus to catch up with the passer-by is known, the speed of the bus is known; the speed of approach is unknown; the desired value is the speed of the passerby).

5) How to determine unknown quantities?

Here, just as in the case of the hat problem, the second solution is shorter, but more difficult to come up with. Therefore, you should not rush to give children a ready-made solution; the effect will be minimal. It is better to return to this task over the course of several lessons, giving children the opportunity to become increasingly aware of the situation described in it.

225. a) 1000 liters of gasoline cost 8,500 rubles. Determine the cost of 210 liters of gasoline. Try to solve this problem without converting rubles into kopecks.

b) The worker produced 10 parts on his machine in 52 hours 30 minutes; an automatic machine produced 25 of the same parts in 43 hours and 45 minutes. How many times faster did the machine run than the worker?

a) Hint. Determine the cost of 10 liters of gasoline.

b) A similar technique cannot be applied. But even attempts to do something contribute to the accumulation of experience in working with units of time. Ultimately, we come to the need to express the operating time in minutes.

349. The airplane flew from one point to another with average speed 180 km/h. If his speed was 200 km/h, then he would have spent 30 minutes less on the same journey. Determine the distance between points.

In the textbook there are stepping stone problems leading to problem No. 000. These are problems No. 000-329. Solving these problems leads to the need to perform division with a remainder, to determine what part this remainder is from the value taken as a whole: the distance that is covered per unit of time, or the cost of a unit of mass.

Practice shows that in order for almost all students to solve problem No. 000 in one way or another, several lessons are required. As a rule, 1-2 students come to the first lesson after receiving the task with a solution, and quite often the problem is solved by selection. It should not be rejected. However, students should be encouraged to try to solve the problem using a more traditional method.

An attempt to solve a problem using an equation, as a rule, leads to expressions that students at this stage do not yet know how to convert. Therefore, there is a need to solve this problem using the arithmetic method.

First Hint. What quantities do you need to know to determine the distance? Which ones are known? Imagine that two airplanes take off at the same time: the first at a speed of 180 km/h, and the second at a speed of 200 km/h.

After this clue, several more students come up with solutions.

Second Hint. At what distance from the point of arrival was the first airplane at the moment when the second one arrived there? How would you characterize this distance? It is advisable to build a graphic model of the situation together with students:

Third Hint. The speed is known. What do you need to know to determine the travel time, knowing how far the second airplane overtook the first during this time?

Solution (note that we present only one of the possible methods; practice shows that with such an organization of work on a task, students bring up to five in various ways decisions).

1) Imagine that two airplanes take off at the same time, the first at a speed of 180 km/h, and the second at a speed of 200 km/h. Then, at the moment when the second one landed, the first one was 30 minutes away from its destination. Since his speed is 180 km/h, he only has to fly

180: 2 = 90 (km).

2) 90 km is the distance by which the second airplane overtook the first during the flight. To find the distance between cities, you need to know the flight time. This is the same time during which the second airplane overtook the first by 90 km. It can be found by determining the removal rate:

200 – 180 = 20 (km/h).

3) 90: 20 = 4 hours (10 km rest).

If the distance between planes increases by 20 km in 1 hour, then it will increase by 10 km in half an hour. This means that the second airplane was in flight for 4 hours 30 minutes.

4) 200 × 4 = 800 (km) – the distance that the second airplane flew in 4 hours.

And in another half hour he was ill.

5) So the distance between cities is: 800 + 100 = 900 (km).

Answer. 900 km.

493. Draw a segment MN. Mark the points on it K And L so that the segment KN was , and the segment M.L.– segment MN. What part of the segments MN, N.K., M.L., MK And NL constitutes a segment KL? Before solving a problem, think about what length it is convenient to take a segment MN.

The hint is contained in the text of the problem. Students are asked to read the first two sentences in class and think about the prompt. After this, the task is given at home.

You can even do the first half of the assignment in class: draw a line segment and mark the points on it. Students are asked to complete the assignment at home.

Answer: segment KL is the length of the segment MN, length of the segment N.K., length of the segment M.L., 1 segment length MK, 1 segment length NL.

581. The library needs to bind 960 books. One bookbinding shop can complete this work in 16 days, another in 24 and a third in 48 days. In what time can three workshops complete this work, working simultaneously, and how many books will each workshop have time to bind? Is it possible to distribute books between workshops so that this work can be completed in more short term?

Students have already solved problems on working together, but there were still two workers (No. 000, 143, 157), the solution was related to fractions (No. 000, 518, 519). Therefore, in a lesson, when this task is given at home, students should be given the opportunity to read the condition and think about the question: what do they need to know in order to determine how long it will take three workshops to complete the work, working simultaneously? There are two possible answers: 1) how many books can three workshops bind in one day, working simultaneously; 2) what part of the work can three workshops complete in one day, working simultaneously ( ). However, in 5th grade the second option is unlikely. This method of solution can be considered in the 6th grade, returning to this problem in the second half of the year, when students will be familiar with all the operations with ordinary fractions.

1) How many books can the first workshop bind in one day?

960: 16 = 60 (books).

2) How many books can the second workshop bind in one day?

960: 24 = 40 (books).

3) How many books can the third workshop bind in one day?

960: 48 = 20 (books).

4) How many books can three workshops bind in one day, working simultaneously?

60 + 40 + 20 = 120 (books).

5) How long will it take three workshops to complete the work, working simultaneously?

960: 120 = 8 (days).

6) How many books will the first workshop manage to bind in 8 days?

60 × 8 = 480 (books).

7) How many books will the second workshop manage to bind in 8 days?

40 × 8 = 320 (books).

6) How many books will the third workshop manage to bind in 8 days?

20 × 8 = 160 (books).

Note that the first 5 actions can be written in one expression.

The second question of the task can be rephrased as follows: will the work be completed in a shorter time if given more books to the workshop that works the fastest? (Because obviously, if the books are given to a workshop that works slower, the work will take longer to complete).

The answer to the first question of the problem was:

a) the work will be completed in 8 days;

b) in 8 days, workshop I will have time to bind 480 books;

Workshop II will have time to bind 320 books;

Workshop III will have time to bind 160 books.

If you redistribute the books, increasing their number in workshop I, then the work will take more than 8 days. This means that only the found distribution option is optimal.

In fact, the fact that increasing the number of books in the first workshop leads to an increase in the completion time is quite obvious, but some students remain doubtful if the results found in answering the first question are not clearly presented to them.

Let’s take the volume of all work as one – 1. Then in one day

I workshop will be able to perform part of the total work,

Workshop II will be able to perform part of the total work,

Workshop III will be able to perform part of the total work,

1) What part of the work can be completed in one day by three workshops working simultaneously?

(part of the work)

2) Part of the work is completed in one day, which means that all the work will be completed in 8 days.

3) How many books will each workshop manage to bind in 8 days?

Workshop I: (part);

Workshop II: (part);

III workshop: (part).

4) How many books will each workshop manage to bind in 8 days?

Workshop I: 960 × = 480 (books);

Workshop II: 960 × = 320 (books);

III workshop: 960 × = 160 (books).

Answer: 8 days, Workshop I will have time to bind 480 books, Workshop II – 320 books, Workshop III – 160 books.

677. The first flask contains 3 times more milk than the second. When 15 liters were poured from the first flask into the second, the milk in both flasks became equal. How many liters of milk were in each flask initially?

An attempt to solve the problem using the algebraic method leads to an equation that is quite difficult for fifth-graders to solve. Therefore, here it is advisable to invite students to create a graphic model of the situation (drawing) described in the problem and think about this model:

Leading question: show the amount of milk that needs to be poured from the first can into the second in order to equalize the amount of milk in both cans.

Once the students realized that 15 liters is a third of the milk contained in the first can, the problem is solved.

678. 1) Solve the problem by selection. Of the 29 boxes, some contain 14 kg of sweets, and some contain 15 kg. How many of these and other boxes if total mass Are the chocolates in both types of boxes the same?

2) Come up with a similar problem yourself.

Hint: Study the data carefully.

Having carefully studied the data, we see that 14 + 15 = 29. This means that there should be 15 boxes containing 14 kg each, and 14 boxes containing 15 kg each.

689. A passenger on a train traveling at 50 km/h noticed that an oncoming train passed him within 10 seconds. Determine the length of the oncoming train if its speed is 58 km/h.

What quantities are known in the problem? Let's make a drawing:

The length of the train is the distance from the beginning of the head car to the end of the tail car. What quantities do we usually use to find distance?

How would you solve the problem if the train in which the passenger was sitting stood still?

1) 50 + 58 = 108 km/h the speed with which the oncoming train passed the passenger.

2) 108 (km/h) = (108 × 1000) : 3600 (m/s) = 30 (m/s).

3) 30 × 10 = 300 (m) – length of the train.

Answer: 300 m.

690. A). From the pier A A boat set off down the river. At the same time from the pier IN a second boat came out to meet him with the same speed. The first boat reached the pier IN in 4 hours. At what distance from the pier A was there a second one at that time if the current speed is 2 km/h?

b) In case of difficulties, try to determine how many more kilometers the first boat travels in 1 hour than the second

c) If you were still unable to solve the problem, try to figure out how this can be done from the following text.

The first boat, when moving downstream in 4 hours, “gained” 8 km (4 × 2) compared to the distance that it would have covered during this time, moving in still water, and the second boat “lost” the same number of kilometers, since moved against the current. In total, the second boat “lost” 16 km to the first in 4 hours. This means that he was at such a distance from A when the first one arrived at B.

Hints and the solution to this problem follow immediately after the condition, under letters b) and c).

¢798. Using a compass, draw a circle and draw the diameter. Label it AB. Mark any two points on the circle WITH And D. Connect them with the dots A And IN. What kind of angles (sharp, straight or obtuse) did you get? DIA And A.D.B.? Draw a conclusion.

799. Draw a circle and draw a line segment AB with ends on this circle. Mark points on the circle C, D And E so that the angle ABC was sharp, the angle ABD- straight, and the angle ABE- stupid.

Problems No. 000 and 799 are stepping stones to Problem No. 000.

When completing task No. 000, students see that all angles whose vertices belong to a circle and whose sides pass through the ends of the diameter are straight.

After completing task No. 000, it is advisable to ask students the question: “Are there any A.C., AD And A.E. diameter of a given circle?

800. On a separate sheet of paper, using a cup instead of a compass, draw a circle with a pencil. Cut out the resulting circle and think about how to find its center using bending. Think about how to find the center of a circle if the circle cannot be bent.

Performing the first task - finding the center of the cut out circle by bending it, as a rule, does not cause any difficulties.

If the circle cannot be bent, then it is more difficult to find the center. Here, students should be asked to think about which of the properties of angles and circles that they became familiar with in previous assignments (No. 000, 799) can be used in this problem. It turns out that it is enough to construct a right angle BAC, where the points A, B, C belong to the circle, then B.C. is the diameter, and its midpoint is the center of the circle.

We recommend that the teacher be sure to review these problems with students, since in grade 6 they will be offered tasks of this type: the picture shows a circle whose center is not marked, and you need to determine the length of this circle by measuring its diameter or radius.

If students are not familiar with how to determine the diameter or radius of a circle whose center is unknown, they will have a difficult time completing this task.

846. Find the length of the fence surrounding a rectangular house, 15.5 m long and 4.8 m wide, if the fence is placed at a distance of 10 m from it.

For this task, it is advisable to make a schematic drawing so that, in particular, it is clear what is meant by the distance from the house to the fence:

879. The boat, having met the raft, continued moving for another half hour in the same direction, and then turned around and headed back. How long will it take him to catch up with the raft?

This task is difficult even for high school students. But since they are familiar with the transformation literal expressions, in most cases they manage to get the correct answer.

As a rule, fifth-graders either bring the solution in letter form that their parents made, or make some assumptions that they have difficulty justifying, or they give some values ​​for the speed of the boat and the current and solve the problem with numerical data.

The last option, in our opinion, is the most acceptable. Students should be asked to ask different meanings for boat speeds and currents and solve the problem with these data. In all cases the same result is obtained. After this, students express the assumption that the result does not depend on the numerical data. The teacher asks you to think - why?

Justifications can take different forms. Let's give one of them.

The speed of the boat moving away from the raft (moving against the current):

(v own boats – v currents) + v raft(current) = v own boats.

Speed ​​of approach between the boat and the raft (moving with the current):

(v own boats + v currents) – v raft(current) = v own boats.

1008. Give a counterexample to the statement: any two rectangular parallelepiped, having equal volumes, have and equal areas surfaces.

Hint: You can use cubes for clarity. For example:

1021. A passenger on a train traveling at a speed of 79.2 km/h noticed that an oncoming train passed him for 12 s. Determine the speed of the oncoming train if its length is 480 m.

This problem is very similar to problem No. 000. Only there the speeds of both trains were given, and it was necessary to find the length of the oncoming train; here the length is known, but the speed needs to be found. Therefore, the first hint to this problem may be a suggestion to remember how problem No. 000 was solved.

In addition, you can ask students to think about how they would solve the problem if the train in which the passenger was sitting was standing still; which component and how should be changed, given that the trains were traveling towards each other.

1) Let us express the speed of the train in which the passenger was traveling in meters per second:

79.2 (km/h) = (79.2 × 1000) : 3600 (m/s) = 22 (m/s).

2) 480: 12 = 40 (m/s) – the speed at which the oncoming train passed the passenger.

3) 40 – 22 = 18 (m/s) – speed of the oncoming train.

4) Express the speed of the oncoming train in km/h:

(18 × 3600): 1000 = 64.8 (km/h).

Answer: 64.8 km/h.

After the problem is solved, you can ask students to come up with a problem for the following situation: a passenger is sitting on a train, and another train overtakes him on a parallel track.

Stalin even awarded the rank of marshal to Tukhachevsky. But does anyone really consider Tukhachevsky a strategist?

The fact that Stalin awarded orders and titles to Zhukov does not mean anything. Stalin's people's commissars, ministers, marshals and generals included scoundrels, crooks, sadists, debauchees, thieves, and fraudsters. Here you have Yezhov, and Yagoda, and Blucher, and Bukharin, and Radek, and Khrushchev and a whole bunch of others.

GO TO SYCHEVKA!

When it comes to war, we remember Stalingrad, and when we remember Stalingrad, we remember Zhukov. It was he, the greatest commander of the twentieth century, who was the creator of one of the most brilliant operations of the Second World War, and, perhaps, of all world history. Stalingrad is a confirmation of the indisputable truth: where Zhukov is, there is victory! Stalingrad is proof of Zhukov’s genius: he glanced at the map and immediately found a solution!

Let’s shout three times “Hurray” to the genius, and then ask a question about the reliability of the information. Let's get to the roots. Let's establish how it became known that the plan for the Stalingrad strategic offensive operation was proposed by Zhukov?

The source is easy to find: Zhukov himself said this. It was he who declared himself the author of the operation plan, although he admitted that there was also a co-author - A. M. Vasilevsky. It is described like this:

“On the afternoon of September 12, I flew to Moscow and four hours later I was in the Kremlin, where the Chief of the General Staff A.M. Vasilevsky was also summoned...

The Supreme Commander took out his map with the location of General Headquarters reserves and looked at it for a long time and intently. Alexander Mikhailovich and I moved away from the table to the side and talked very quietly about the fact that, apparently, we need to look for some other solution.

What is the “other” solution? - suddenly, raising his head, asked I.V. Stalin.

I never thought that I.V. Stalin had such acute hearing. We approached the table...

The whole next day, A.M. Vasilevsky and I worked at the General Staff... Having gone through all possible options, we decided to propose to Stalin the following plan of action...” (“Memories and Reflections.” M. APN. 1969. P.401-402)

From the above it follows that at the origins of the Stalingrad strategic offensive operation there were three people: Stalin, Zhukov and Vasilevsky. Stalin's merit is that his hearing is sharp. Stalin heard that Zhukov and Vasilevsky were whispering, became interested, and it was then that Zhukov and his comrade in arms gave the Supreme Commander-in-Chief a brilliant idea...

Zhukov said that Stalin doubted success, was afraid to take risks, and proposed carrying out an operation, but not on such a scale, but more modestly. But Zhukov persuaded Stalin, and everything turned out as it should.

About Stalingrad, through the mouths of his literary blacks, Zhukov speaks in detail and at length: “On July 12, the headquarters created a new Stalingrad Front...” “By the end of July, the Stalingrad Front included...” “The regional committee and the city party committee of Stalingrad carried out a lot of organizational work on the formation and preparation of the people’s militia... »

All this is true, all this is interesting, but let us pay attention to a small detail: in July 1942, Zhukov was not in Stalingrad and could not have been. He was in a completely different direction, very far from Stalingrad. Anyone who is interested in the war has the opportunity to reconstruct the chronology of Zhukov’s work at the front day by day, from the first to the last day of the war. Sometimes - accurate to hours and minutes. From October 11, 1941 to August 26, 1942, Zhukov commanded the troops of the Western Front, which fought in a completely different direction, a thousand kilometers from Stalingrad.

On the night of September 14-15, 1942, the 13th Guards rifle division under the command of General Rodimtsev, she crossed from the left bank of the Volga to the center of Stalingrad, when the fate of the city was being decided in a fierce battle with the enemy. The 13th Guards fought in Stalingrad for 140 days and nights. Its fighters defended Pavlov's House, fought for the central railway station and Mamayev Kurgan. Marshal Nikolai Krylov, chief of staff of the legendary 62nd Army during the defense of Stalingrad, wrote in his memoirs: “The glory given to the guardsmen of Major General Rodimtsev is well deserved by them. If they had not crossed that night, it might have turned out that there was nowhere to cross. If we managed to prevent the enemy from cutting through the remnants of our army and establishing a foothold on the Central Embankment on September 14, then we would probably be able to hold back the next enemy onslaught of such force (and now from the initial positions, which were in some places a little over a kilometer from the Volga) without receiving reinforcements by the morning. , they couldn’t... The reinforcements were not late, and this made it possible to hold the city. For eleven days - until the Nazi command changed the direction of the main attack - Rodimtsev’s division played a decisive role in the defense of Stalingrad.” The crossing was carried out on motor ferries, minesweepers, armored boats, tugboats and even fishing boats. The boat, which had a company of machine gunners on board, was killed by artillery fire, and there were losses on other ships as well. Artillery regiment of the 13th division, which took firing positions on the left bank, was able, like other artillery stationed beyond the Volga, to support the infantry only when its front edge was more clearly defined.

In many places between the embankment and the railway, something like a layer cake was created: houses, courtyards, shelters captured by the Nazis and held by us were located interspersed. Staff operators did not always know which pencil - red or blue - to circle such and such a building on the city plan. This is how Krylov recalled his first meeting with Rodimtsev: “I don’t remember exactly at what time the 13th Guards Divisional Commander Alexander Ilyich Rodimtsev reached the army command post. In any case, by that time his regiments had already gone significantly deeper into the city, clearing the water pumping station, department store, nail factory and other objects from the Nazis (the House of Specialists continued to be held by an isolated group of Germans). The guide who accompanied Rodimtsev was killed on the way. The division commander himself must have had to take refuge in ruins or craters more than once, and he, like everyone else who came from the city, entered the dungeon, shaking off lime and dust. Chuikov (Vasily Chuikov, commander of the 62nd Army - author) asked Rodimtsev what his mood was here in Stalingrad. Alexander Ilyich replied: “I’m a communist and I’m not going anywhere from here.” Meanwhile, the position of the division, or more precisely, its two regiments that had crossed, became more and more difficult with each passing hour. The guardsmen reached the line passing through the city railway, but they did not have time to gain a foothold there before the enemy resumed the offensive. The enemy, having not decided on a major attack at night, although he missed the moment when we actually had only small detachments left in the city center, now had a huge numerical superiority: each of Rodimtsev’s regiments was opposed by a division, reinforced by a significant number of tanks. And as usual, the Nazi attacks were preceded by massive air strikes.” None of those who fought in Stalingrad yet knew that at Headquarters at that time work had already begun to prepare a large-scale counter-offensive near Stalingrad.

This is where it all began, according to the memoirs of Marshal Georgy Zhukov: “The Supreme Commander took out his map with the location of General Headquarters reserves and looked at it for a long time and intently. Alexander Mikhailovich (Vasilevsky, Chief of the General Staff of the Red Army - author) and I moved away from the table to the side and very quietly talked about the fact that, apparently, we need to look for some other solution. - What is the “other” solution? - J.V. Stalin suddenly raised his head and asked. I never thought that I.V. Stalin had such acute hearing. We approached the table. “That’s what,” he continued, “go to the General Staff and think carefully about what needs to be done in the Stalingrad area.” Where and what troops can be transferred from to strengthen the Stalingrad group, and at the same time think about the Caucasian Front. Tomorrow at 9 o'clock in the evening we will gather here again... Having gone through all possible options, we decided to propose to I.V. Stalin the following plan of action: first, continue to wear out the enemy with active defense; the second is to begin preparing a counteroffensive in order to inflict such a blow on the enemy in the Stalingrad area that would dramatically change the strategic situation in the south of the country in our favor. As for the specific plan for the counteroffensive, naturally, we could not prepare detailed calculations in one day, but it was clear to us that the main attacks needed to be delivered on the flanks of the Stalingrad group, covered by the royal Romanian troops. Approximate calculations showed that it would be impossible to prepare the necessary forces and means for a counter-offensive before mid-November.”

On November 19, 1942, the plan for the offensive operation, called “Uranus,” began to be implemented. The idea of ​​​​breaking through the positions of the Romanian royal troops turned out to be brilliant and fully justified itself. “Another solution,” the conversation about which Stalin overheard Zhukov and Vasilevsky, turned out to be one of the most successful in the history of the Red Army...