Solving problems on WEIGHING. 1. Comparison tasks using scales. - presentation

Task 1
To dilute instant mashed potatoes “Green Giant” you need 1 liter of water. How, having two vessels with a capacity of 5 and 9 liters, pour 1 liter of water from a water tap?

Problem 2

How to measure exactly 1 liter using 2-liter and 5-liter jars?

Problem 3

How, with a five-liter bucket and a nine-liter jar, can you collect exactly three liters of water from the river?

Problem 4

For a forced march through the desert, a traveler needs to have 4 liters of water. He can't take any more. At the base where there is a water source, only 5-liter flasks are issued, and 3-liter cans are also available. How to fill a flask with 4 liters using one flask and one jar?

Problem 5

There are two jugs with a capacity of 5 l and 9 l. You need to collect 7 liters of water from a source if you can only use jugs.

Problem 6

Measure out 3 liters using a 5 liter container. What is the minimum number of transfers required to pour 3 liters of water into a four-liter saucepan using a tap and a five-liter jar?

Problem 7

Divide 10 liters equally, having vessels of 3, 6 and 7 liters. Divide the water in a 6-liter vessel (4 l) and a 7-liter vessel (6 l) into 2 equal parts, using these and a 3-liter vessel. What is the least number of transfusions required?

Problem 8

Divide 8 liters equally, having vessels of 8, 5 and 3 liters. Divide the water in a full 8-liter vessel into two equal parts, using this and empty 5- and 3-liter vessels. What is the least number of transfusions required?

Problem 9

Divide 16 liters equally, having vessels of 6, 11 and 16 liters. Divide the water in a full 16-liter vessel into two equal parts, using this and empty 11- and 6-liter vessels. What is the least number of transfusions required?

Problem 10

Two vessels and a tap with water. What is the minimum number of transfusions necessary to measure 2 liters using 7- and 11-liter vessels and a water tap?

Problem 11

A fast river flows next to the laboratory. Using two barrels of 3 and 5 gallons, how can you measure exactly 4 gallons of river water?

Problem 12

Cepustrolis has an insoluble flask containing 12 milliliters of sulfuric acid, as well as two insoluble beakers with a volume of 5 and 7 milliliters. How can he get two portions of 6 milliliters of sulfuric acid needed for the experiment? (The acid will dissolve any other glassware in the laboratory.) Note Solution

Problem 13

One day, an alchemist managed to collect and mix 8 salamander tears (the most important alchemical substance) in one vessel. He has two empty bottles with a volume of 2 and 3 tears. How can he measure out 4 tears? Don't forget that tears dry very quickly! Cepustrolis only has time for three transfusions before the rare substance evaporates.

Problem 14

Another important element of the elixir is cobra blood. There are 10 spoons of snake blood collected in a bowl. There are 3 scoop and 4 scoop ladles available. How can a scientist get 5 spoons of blood? When solving the problem, remember that you need to do no more than 5 transfusions, otherwise the precious blood will clot and cease to be useful.

Problem 15

In the basement of the laboratory, mandrakes grow and there is an unlimited supply of mandrake extract. How to measure 4 milliliters of mandrake extract using the beakers from problem No. 2? But beware! If at any stage there is not exactly 3 milliliters of extract in any of the beakers, the mandrakes will throw a tantrum and destroy the laboratory with screams!

Problem 16

In the laboratory furnace there is a cauldron in which 9 liters of molten tin are bubbling. During the experiment, you need to add 3 liters of tin to the elixir three times at regular intervals. How to do this if there are only three fireproof cups with a volume of 5, 4 and 2 liters? (That is, you need to have 3 servings of 3 liters at some point.)

Problem 17

Measure out 3 liters using a 5 liter container. What is the minimum number of transfers required to pour 3 liters of water into a four-liter saucepan using a tap and a five-liter jar?

Problem 18

One day Winnie the Pooh wanted to eat honey and went to visit the bees. On the way, I picked a bouquet of flowers to give to the working bees. The bees were very happy to see the bear with a bouquet of flowers and said: “We have a big barrel of honey. We will give you honey if you can pour yourself 4 liters using two vessels with a capacity of 3 liters and 5 liters!” Winnie the Pooh thought for a long time, but was still able to solve the problem. How did he do it?

Problem 19

Batman and Spider-Man couldn't decide which of them was the most important superhero. Whatever they did: push-ups, ran the 100-meter dash, did pull-ups - first one would win, then the other. Without resolving their dispute, they went to the sage. The sage thought and said: “The most important superhero is not the one who is stronger, but the one who is smarter! Whoever solves the problem first will be the best! Listen: there are two vessels with a capacity of 8 liters and 5 liters. How can you use these vessels to pour 7 liters of living water from a source?” Help your favorite hero solve this problem.

Problem 20

A 10 liter can can is filled with fresh milk. It is required to pour 5 liters of milk from this can into a seven-liter can, using a three-liter can.

Problem 21

Divide the water in a 6-liter vessel (4 l) and a 7-liter vessel (6 l) into 2 equal parts, using these and a 3-liter vessel. What is the least number of transfusions required?

Problem 22

Uncle Fyodor was getting ready to go visit his parents and asked the cat Matroskin for 4 liters of yogurt milk. And Matroskin has only 2 empty cans: a three-liter and a five-liter. And an eight-liter bucket filled with milk. How can Matroskin pour 4 liters of milk using the existing vessels?

Problem 23

At the foot of a high hill, on the bank of a quiet river, there was a small village. Two hunter brothers lived there. The older brother's name was Kaalka, the younger brother's name was Kopchon. The elder brother sends the younger brother for water and gives him two wineskins, with a capacity of 8 liters and 5 liters, and asks him to bring exactly 7 liters of water. Will Kopchon be able to fulfill his older brother's request?

Problem 24

Tom Sawyer needs to paint the fence. He has 12 liters of paint and wants to cast half of this amount, but he does not have a vessel with a capacity of 6 liters. He has 2 vessels: one with a capacity of 8 liters, and the other with a capacity of 5 liters. How to pour 6 liters of paint into an 8 liter container? What is the minimum number of transfusions required?

Problem 25

SpongeBob urgently needs to pour 6 liters of water from the tap. But it has only two vessels: 5-liter and 7-liter. How can he do this?

Problem 26

There is a six-liter jar of juice and two empty jars: three- and four-liter. How to pour 1 liter of juice into a three-liter jar?

Problem 27

Two people must equally share 8 buckets of kvass in an eight-bucket barrel. But they only have two empty barrels, one of which holds 5 buckets and the other holds 3 buckets. The question is, how can they separate this kvass using only these three barrels?

Problem 28

There are three barrels with a capacity of 6 buckets, 3 buckets and 7 buckets. The first and third contain 4 and 6 buckets of kvass, respectively. It is required, using only these three barrels, to divide the kvass equally.

Problem 29

Three people purchased a jar completely filled with 24 ounces of balm. They later purchased three empty containers of 5, 11 and 13 ounces. How could they divide the balm into equal parts using these four vessels? Try to solve the problem in the least number of transfusions.

Problem 30

There is a three-liter jar of juice and two empty jars: one is a liter, the other is two-liter. How to pour the juice so that all three jars contain one liter?

Problem 31

In one port, a sailor came to a store with an empty five-gallon barrel and asked the storekeeper to fill it with four gallons of selected Jamaican rum. Unfortunately, the only vessel for measuring was an old three-gallon tin jug. How did the shopkeeper manage to accurately measure four gallons using these two containers?

Problem 32

The seller, a mathematics student who works part-time in the summer selling a barrel of kvass, is approached by two cheerful friends and asks to pour them a liter of kvass each. The seller notices that he only has two containers, a three-liter and a five-liter, and he cannot fulfill their request. The friends offer $100 if the seller can fulfill their order, and the seller must give them portions at the same time. After some thought, the seller managed to do it. How? Note that kvass is not lost during transfusion and that full containers allow you to accurately measure volumes of 3 and 5 liters.

Problem 33

A winemaker usually sells his wine in 30 and 50 liter bottles and only uses jugs of this size. One of the buyers wanted to buy 10 liters. How did the winemaker measure out 10 liters for him using his jugs?

Problem 34

How to cast half from a full vessel with a capacity of 12 liters, using two empty vessels with a capacity of 8 and 5 liters?

Problem 35

Shrek decided to give Fiona a birthday present - to cook the soup that she had been dreaming about for a long time. He found the recipe for this soup in a cookbook, but there was a small problem: he needed to pour exactly 5 liters of water into the pan. But how to do this if Shrek has a 7-liter bucket and a 3-liter jar? Help your favorite hero make Fiona's dream come true.

Problem 36

Harry Potter has two hourglasses: one at 7 minutes and one at 11 minutes. The magic potion should be brewed for 15 minutes. How can Harry Potter cook it by turning the clock over the minimum number of times?

Problem 37

In the summer, Winnie the Pooh stocked up on honey for the winter and decided to divide it in half so that he could eat half before the New Year and the other half after the New Year. All the honey is in a bucket that holds 6 liters, it has 2 empty jars - a 5 liter and a 1 liter. Can he separate the honey the way he intended?

Problem 38

Snow White has a full eight-liter bucket of compote. How can she pour 4 liters using an empty three-liter jar and a five-liter can?

Problem 39

The owner has four barrels A, B, C and D, and barrels C and D are of the same capacity. Let barrels A and B be filled with kvass, if barrel C is filled with the contents of barrel A, then 1/5 of its contents will remain in barrel A, but if barrel D is filled with the contents of barrel B, then 1/9 of its contents will remain in barrel B. Let barrels C and D be filled with kvass; to fill barrels A and B, you need to take the contents of barrels C and D and add another 9 buckets of kvass. How many buckets of kvass can each barrel hold?

Problem 40

From a bucket containing 5 liters of water, 1 liter is poured, and then 1 liter of juice is poured into the bucket. Having mixed all this, 1 liter of the mixture is poured from the bucket, then 1 liter of juice is poured into the bucket again. Mix again, pour 1 liter of the mixture and pour in 1 liter of juice. How much water will remain in the bucket after this?

Problem 41

From a barrel containing 100 liters of juice, 1 liter is poured and then 1 liter of water is poured into it. After mixing the resulting mixture, 1 liter of the mixture is poured from the barrel and 1 liter of water is again poured into it. Having mixed the resulting mixture, one liter of the mixture is again poured from the barrel and 1 liter of water is poured in, and this is done repeatedly. Is it possible, as a result of such operations, to obtain a mixture containing 50 liters of water and 50 liters of juice?

Problem 42

Two groups of climbers are preparing for the ascent. To prepare food, they use primus stoves, which are filled with gasoline. The climbing camp has a 10-liter canister of gasoline. There are also empty vessels of 7 and 2 liters. How to pour gasoline into two containers of 5 liters each?

Problem 43

The robbers obtained 10 ounces (1 ounce - approximately 30 cm 3) of gold dust. They have two empty boxes, 6 oz and 4 oz. How can they split the sand in half? If it takes 1 minute for one pour, how long will it take them to divide their prey?

Problem 44

Pour 13 liters of milk from the tank using cans with a capacity of 17 liters and 5 liters.

Problem 45

Tom Sawyer needs to paint the fence. He has 12 liters of paint and wants to cast half of this amount, but he does not have a vessel with a capacity of 6 liters. He has 2 vessels: one with a capacity of 8 liters, and the other with a capacity of 5 liters. How to pour 6 liters of paint into an 8 liter container? What is the minimum number of transfusions required?

Problem 46

To dilute Green Giant instant mashed potatoes, you need 1 liter of water. How, having two vessels with a capacity of 5 and 9 liters, pour 1 liter of water from a water tap?

Problem 47

During the hike we prepared a bucket of compote. How, having jars holding 500 g and 900 g of water, pour compote in portions of 300 g?

Problem 48

Oil workers drilled an oil well. It is necessary to deliver 6 liters of oil to the laboratory for examination. Available in 9 liter and 4 liter containers. How can you collect 6 liters using these vessels?

Problem 49

Look at the shore - there you will see two banks. One of them holds exactly two liters of water, and the other - three. How to pour exactly one liter into a two-liter jar? Give two ways.

Problem 50

There are three cans with a capacity of 14, 9 and 5 liters. The large can contains 14 liters of milk, the rest are empty. How can you use these cans to split milk in half?

Problem 51

There are three vessels without divisions with volumes of 6 l, 7 l, 8 l, a water tap, a sink and 6 l of syrup in the smallest vessel. Is it possible to use transfusions to obtain 12 liters of a mixture of water and syrup, so that each vessel contains equal amounts of water and syrup?

Problem 52

There are two vessels with a capacity of 7 and 11 liters and a large barrel filled with water. How can you measure exactly 2 liters of water using these two vessels?

Problem 53

There are three vessels with a capacity of 8, 5 and 3 liters. The largest vessel is full of milk. How to divide this milk into two equal parts using the remaining vessels?

Problem 54

At the foot of a high hill, on the bank of a quiet river, there was a small village. Two hunter brothers lived there. The elder brother sends the younger brother for water and gives him two wineskins, with a capacity of 8 liters and 5 liters, and asks him to bring exactly 7 liters of water. How to do it?

Problem 55

For a forced march through the desert, a traveler needs to have 4 liters of water. He can't take any more. At the base where there is a water source, only 5-liter flasks are issued, and 3-liter cans are also available. How to fill a flask with 4 liters using one flask and one jar?

Problem 56

Take 1 liter of water in any of the vessels. The volumes of the vessels are 5 and 3 liters.

Problem 57

Take 1 liter of water in any of the vessels. Vessel volumes are 8 and 5 liters.

Problem 58

Take 7 liters of water. Vessel volumes - 6, 10, 15 liters.

Problem 59

Take 1 liter of water. The volumes of the vessels are 6 and 10 liters, the first vessel contains 3 liters.

Problem 60

The hero approached the river with two buckets holding 15 liters and 16 liters. Will he be able to pour (measure) exactly 8 liters of water using these buckets?

Problem 61

The milkmaid brought milk in an eight-liter bucket, but the grandmother has only one three-liter jar and one four-liter bucket. How can she get 4 liters of milk from a thrush?

Problem 62

Pour exactly 13 liters of kvass from the barrel using two cans: one with a capacity of 17 liters, and the other with a capacity of 5 liters.

Problem 63

The barrel holds 12 buckets of water. For watering in the evening it was filled to the top. There are two empty barrels that can hold 5 buckets and 8 buckets of water. Pour the contents of the barrel equally.

Problem 64

The canister contains at least 10 liters of kerosene. Is it possible to pour 6 liters of kerosene from it using a nine-liter and a five-liter canister?

Problem 65

A six-liter bucket contains 4 liters of fresh milk, and a seven-liter bucket contains 6 liters. How to pour exactly 1 liter from a six-liter bucket using another three-liter jar?

Problem 66

There are 8 liters of soup in a saucepan. There are also empty 3 and 5 liter jars. You need to measure out 4 liters of soup. How to do this if the soup cannot be spilled?

Problem 67

Mrs. Brain decided to please Erudite and prepared him kvass. The erudite said that he would take only 4 liters of kvass, no more and no less. Mrs. Brain has only 2 vessels at home with a volume of 8 and 5 liters. How can Mrs. Brain, using two vessels with a volume of 8 and 5 liters, pour exactly 4 liters of kvass to Erudite?

Problem 68

There are 2 vessels. The capacity of one is 9 liters, the other is 4 liters. How can you use them to get 6 liters of water from a tank? The water can be drained back into the tank.

Problem 69

To travel by sea you need a supply of fresh water. When swimming, water is consumed at a rate of 1 barrel per day. At some point in time, the water supply on the shore was 8 barrels, and the water was in a tank filled to the brim. The yacht has the same tank, with a capacity of 8 barrels, but empty. How many days can you plan a trip for if you can’t take extra water with you, and you have two more empty containers with a capacity of 3 and 6 barrels at your disposal and they can be used to transfer water?

Problem 70

There are 20 liters of wine in a barrel. A neighbor asks to pour him 5 liters and he himself came with buckets of 7 and 13 liters. No problem, said the owner. How did he do it?

Problem No. 2. Winnie the Pooh and the bees.

One day Winnie the Pooh wanted to eat honey and went to visit the bees. On the way, I picked a bouquet of flowers to give to the working bees. The bees were very happy to see the bear with a bouquet of flowers and said: “We have a big barrel of honey. We will give you honey if you can pour yourself 4 liters using two vessels with a capacity of 3 liters and 5 liters!” Winnie the Pooh thought for a long time, but was still able to solve the problem. How did he do it?

How can you get 4 liters as a result? You need to pour 1 liter from a 5-liter vessel. And how to do it? You need to have exactly 2 liters in a 3-liter container. How to get them? – From a 5-liter vessel, pour 3 liters. It is better and more convenient to present the solution in the form of a table:

Fill a 5-liter vessel with honey from a barrel (step 1). From a 5-liter vessel, pour 3 liters into a 3-liter vessel (step 2). Now there are 2 liters of honey left in the 5-liter vessel. Pour the honey from the 3-liter vessel back into the barrel (step 3). Now from a 5-liter vessel we pour those 2 liters of honey into a 3-liter vessel (step 4). Fill a 5-liter vessel with honey from a barrel (step 5). And from a 5-liter vessel we add honey to a 3-liter vessel. We get 4 liters of honey in a 5-liter vessel (step 6). The problem is solved. The search for a solution could begin with the following action: add 1 liter to three liters. But then the solution will look like this:

Problem No. 8. Tom Sawyer.

Tom Sawyer needs to paint the fence. He has 12 liters of paint and wants to cast half of this amount, but he does not have a vessel with a capacity of 6 liters. He has 2 vessels: one with a capacity of 8 liters, and the other with a capacity of 5 liters. How to pour 6 liters of paint into an 8 liter container? What is the minimum number of transfusions required?

Problem No. 6. Milk from Prostokvashino.

Uncle Fyodor was getting ready to go visit his parents and asked the cat Matroskin for 4 liters of yogurt milk. And Matroskin has only 2 empty cans: a three-liter and a five-liter. And an eight-liter bucket filled with milk. How can Matroskin pour 4 liters of milk using the existing vessels?

Pour 5 liters of milk from an 8-liter bucket into a 5-liter one. Pour 3 liters from a 5-liter can into a 3-liter can. Now pour them into an 8-liter bucket. So now the 3 liter bucket is empty, the 8 liter bucket contains 6 liters of milk, and the 5 liter bucket contains 2 liters of milk. We pour 2 liters of milk from a 5-liter can into a 3-liter can, and then pour 5 liters from an 8-liter bucket into a 5-liter can. Now there is 1 liter of milk in an 8-liter container, 5 liters in a 5-liter container, and 2 liters of milk in a 3-liter container. We top up the 3-liter can from the 5-liter one and pour these 3 liters into the 8-liter bucket. The 8-liter bucket became 4 liters, the same as the 5-liter can. The problem is solved.

After transfusion, it turned out that there were 4 liters of milk in 8-liter and 5-liter vessels, and this was what was required.

Task No. 7.
Collect 7 liters of water from the river.
At the foot of a high hill, on the bank of a quiet river, there was a small village. Two hunter brothers lived there. The older brother's name was Kaalka, the younger brother's name was Kopchon. The elder brother sends the younger brother for water and gives him two wineskins, with a capacity of 8 liters and 5 liters, and asks him to bring exactly 7 liters of water. Will Kopchon be able to fulfill his older brother's request?