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Snap Like Nuts: 10 Short Problems You Don't Have to Think About
Recreation / / December 29, 2020
– 1 –
Kolya, Sasha and Lyosha were fishing. Each of them caught a different number of fish. Sasha and Kolya fished out six of them together, Lyosha and Kolya - four. How many fish did Lyosha catch?
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Each of the guys caught a different number of fish. This means that Lyosha and Kolya could have fished out one or three fish. If Kolya got three pieces, then Sasha would receive the same, and this contradicts the condition. This means that Lyosha caught three fish, Kolya - one, and Sasha - five.
– 2 –
A part is turned from a metal blank. The chips from the eight parts can be remelted to create another piece. How many parts can you make with 64 blanks at the start?
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64 parts can be turned from 64 blanks. The resulting chips can be remelted into 64 ÷ 8 = 8 parts. When making them, one more detail will turn out. In total, 64 + 8 + 1 = 73 parts will be released.
– 3 –
One eraser, two pencil and three notebooks cost 380 rubles. Three erasers, two pencils and one notebook cost 220 rubles. What is the price of a set of eraser, pencil and notepad?
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Four erasers, four pencils and four notebooks cost 380 + 220 = 600 rubles. This means that the price of one set of accessories is 600 ÷ 4 = 150 rubles.
– 4 –
Aliens reported earthlingsthat in the system of their star there are three planets: A, B, C. They live on the second planet. Then the signal worsened, but two more messages were received, which, as scientists established, are both false:
A - not the third planet from the star;
B is the second planet.
What is the name of the planet on which the aliens live?
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Since the two received messages from aliens are false, their meaning must be reversed. Here's what you get:
A - the third planet from the star;
B is not a second planet.
This means that the second planet will be B, on which the aliens live.
– 5 –
The boy and the piglet weigh about five crates. A piglet weighs as much as four cats. Two cats and the piglet weighs like three crates. How many cats will balance a boy?
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A piglet weighs as much as four cats. Two cats and a piglet weigh three crates. So six cats weigh as much as three crates. From this it becomes clear that two cats weigh as much as one box, and one piglet weighs as two boxes. Therefore, the boy weighs as much as three boxes, six cats will balance him.
– 6 –
Two excavators in 2 hours of work will dig a ditch 2 m long. How many excavators do you need to make a 5 m ditch in 5 hours?
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The result of excavators' work per hour is 1 m of a ditch. This means that in 5 hours the same two excavators will dig a 5-meter ditch.
– 7 –
Clock with arrows are 6 minutes behind every day. How many days later will they show the correct time again?
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The clock lags behind every day by 6 minutes, at 1 hour 60 minutes. Let's calculate how many days the clock will lag behind by 1 hour: 60 ÷ 6 = 10 days. The clock with hands has 12 divisions. Let's find out how many days it will take for them to be 12 hours behind: 12 × 10 = 120 days. After this period, the clock will start showing the correct time again.
– 8 –
Three friends met: Belov, Chernov and Ryzhov. “The hair of one of us is white, the other is black, the third is red, but none of the hair color matches the surname,” said the black-haired man. “You're right,” Belov confirmed. What kind of hair does anyone have?
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Belov confirmed the words of the black-haired, therefore, his own hair is red, not black (they cannot be white by condition). Chernov's hair cannot be red or black, which means it is white. Then Ryzhov is the owner of black hair.
– 9 –
Before king the news came that one of the three heroes killed the Serpent Gorynych. The king ordered them to appear at the court. The heroes said:
Ilya Muromets: "The snake was killed by Dobrynya Nikitich."
Dobrynya Nikitich: "Alyosha Popovich killed the snake."
Alyosha Popovich: "I killed the snake."
It is known that only one hero told the truth, and two cheated. Who killed the snake?
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Dobrynya Nikitich and Alyosha Popovich said the same thing and cheated. Ilya Muromets told the truth. According to him, the killer of the snake is Dobrynya Nikitich.
– 10 –
The brother had six 200-ruble bills, and the sister had 10, 300 rubles each. How many of her bills should a sister give to her brother so that they have equal money?
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The brother has only 6 × 200 = 1,200 rubles, the sister has 10 × 300 = 3,000 rubles. Let x - the amount that the sister must give to the brother. Let's compose an equation and solve it: 3000 - x = 1 200 + x; 2x = 1 800; x = 900. To make the money equal, the sister must give her brother 900 rubles, or three 300-ruble bills.
Conditions and answers are taken from the collection “Tasksthat everyone can solve ”A. FROM. Krylov and A. IN. Butenko, as well as site Small Mechanics and Mathematics of Moscow State University.
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