10 fun tasks to warm up your brain

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Try to solve puzzles from Raymond Smullian, mathematician and author of many books on logic problems.

1. Monetary paradox

Richard and Paul have the same amount of money. How much does Richard have to give Paul to get $ 10 more than him?

Answer: 5 dollars. Many answer 10 dollars and make a mistake. Let's say each friend has $ 50. If Richard gives Paul $ 10, Paul will have $ 60 and Richard only $ 40. Therefore, Paul will have $ 20 more than Richard, not $ 10.

Show answer Hide answer

2. Roof slope

The roof of one house is asymmetrical: one slope of it makes an angle of 60 degrees with the horizontal, the other - an angle of 70 degrees. Suppose a rooster lays an egg on a roof ridge. Where will it fall: towards a flatter or steep slope?

None: Roosters do not lay eggs.

Show answer Hide answer

3. The price of wine

A bottle of wine costs $ 10. Wine is $ 9 more expensive than a bottle. How much does an empty bottle cost?

Answer: 0, 5 dollars or 50 cents. Many people answer $ 1, which is not true. If the bottle really cost that much, then its contents should be $ 9 more expensive - $ 10. This means that the wine, together with the bottle, would have cost $ 11. And if a bottle costs $ 0.50, wine costs $ 9.5, then everything together is just $ 10.

Show answer Hide answer

4. An enterprising merchant

The merchant bought the item for $ 7, sold it for $ 8, then bought it again for $ 9, and sold it again for $ 10. What profit did he make?

Answer: $ 2. Let's say that the trader has $ 100, and during the day he will make only the four described transactions.

First, he pays $ 7 for his purchase, then he will have $ 93. When he sells his purchase for $ 8, he will have $ 101.

Then he will buy the same thing again for $ 9, that is, he will spend $ 9 again on the purchase, as a result of which he has $ 92 left. Finally, he will sell the item for $ 10, and therefore, he will have $ 102.

Show answer Hide answer

5. Treadmill

It takes a snail an hour and a half to crawl clockwise along the stadium's treadmill. When the snail crawls along the same path counterclockwise, then a full circle takes 90 minutes. How can you explain the discrepancy between the results?

There is no discrepancy: an hour and a half does not differ from 90 minutes in duration.

Show answer Hide answer

6. Big and small birds

The pet store sells large and small birds. A large bird is twice as expensive as a small one. The woman bought five large birds and three small ones. If she had bought three large birds and five small ones instead, she would have spent $ 20 less. How much is each bird worth?

The price of one large bird is equal to the price of two small ones, so five large birds will cost the same as 10 small ones. This means that five large birds and three small ones will cost the same as 13 small ones. On the other hand, the price of three large and five small birds is equal to the price of 11 small birds.

Thus, the difference between the price of five large and three small birds turns out to be equal to the difference between the price of 13 and 11 small birds, that is, equal to the price of two small birds. Since two small birds cost $ 20, then the price of one such bird is $ 10.

Therefore, the bill for five large and three small birds will be $ 130. If a woman bought three large and five small birds, she would spend $ 110, which is really 20 less.

Answer: a small bird costs $ 10, a large bird costs $ 20.

Show answer Hide answer

7. The problem of ten favorites

Ten dogs and cats were fed 56 biscuits. Each dog got six biscuits, each cat got five. How many dogs were there and how many cats were there?

There is a solution to this problem, for which neither algebra nor enumeration of options is needed. First, let's feed each of the ten animals five biscuits. There will be six biscuits left. But now all the cats have received their due share! So the six remaining biscuits are for dogs. And since each dog should get one more biscuit, it means that there are six dogs and four cats.

This solution is easy to test. If six dogs eat six biscuits, 36 pieces will be used. Four cats, each of which is content with five biscuits, will eat 20 biscuits. This will add up to 56 biscuits.

Answer: four cats and six dogs.

Show answer Hide answer

8. Mysterious egg

What is the correct way to say: “I don’t see white yolk” or “white yolk”?

It would be more correct to say that the yolk is yellow.

Show answer Hide answer

9. Plain socks

In a dark room there is a wardrobe, in a drawer of which there are 24 red and 24 blue socks. What is the smallest number of socks you need to take from a drawer to make at least one pair of socks of the same color?

Answer: three socks. If you take three socks from the box, then they will either all be the same color, or two socks will be the same color, and the third sock will be different, which will also make it possible to make a pair of monochrome socks.

Show answer Hide answer

10. The issue of international law

Suppose there is a plane crash on the border between the United States and Canada. In which of the two countries should the surviving passengers be buried?

It is hardly worth bury those who survived the plane crash.

Show answer Hide answer

The riddles for this collection are taken from the books by Raymond Smullian The Lady or the Tiger? And Other Logic Puzzle s and What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles.