Problems

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Found: 338

Can the equality \(K \times O \times T\) = \(U \times W \times E \times H \times S \times L\) be true if instead of the letters in it we substitute integers from 1 to 9 (different letters correspond to different numbers)?

Rebus. Solve the numerical rebus \(AAAA-BBB + SS-K = 1234\) (different letters correspond to different numbers, but the same letters each time correspond to the same numbers)

a) An apple is heavier than a banana, and a banana is heavier than a kiwi. What’s heavier – a kiwi or an apple?

b) A mandarin is lighter than a pear, and an orange is heavier than a mandarin. What is heavier – a pear or an orange?

The evil stepmother, leaving for the ball, gave Cinderella a bag in which rice and cous-cous were mixed, and ordered for them to be sorted. When Cinderella was leaving for the ball, she left three bags: one was rice, the other – cous-cous, and in the third – an unsorted mixture. In order not to confuse the bags, Cinderella attached to each of them a sign saying: “Rice”, “Cous-cous” and “Mixture”.

The stepmother returned from the ball first and deliberately swapped all the signs in such a way that on every sack there was an incorrect sign. The Fairy Godmother managed to warn Cinderella that now none of the signs on the bags are true. Then Cinderella took out only one single grain from one sack and, looking at it, immediately worked out what was in each bag. How did she do it?

If yesterday was Thursday, what day will be yesterday for the day after tomorrow?

In Wonderland, an investigation was conducted into the case of a stolen soup. At the trial, the White Rabbit said that the soup was stolen by the Mad Hatter. The Cheshire Cat and the Mad Hatter also testified, but what they said, no one remembered, and the record was washed away by Alice’s tears. During the court session, it became clear that only one of the defendants had stolen the soup and that only he had given a truthful testimony. So, who stole the soup?

In a room, there are 85 balloons – red and blue ones. It is known that: 1) at least one of the balls is red, 2) from each arbitrarily chosen pair of balls at least one is blue. How many red balls are there in the room?

If the Humpbacked Horse does not eat or sleep for seven days, it will lose its magical powers. Suppose he did not eat or sleep for a week. What should he do first of all by the end of the seventh day – eat or sleep, so as not to lose powers?

Among some number of mathematicians, every seventh is a philosopher, and among some number of philosophers every ninth is a mathematician. Who are there more of: philosophers or mathematicians?

Know-it-all came to visit the twin brothers Screw and Nut, knowing that one of them never speaks the truth, and asked one of them: “Are you Screw?”. “Yes,” he replied. When Know-it-all asked the second brother the same question, he received an equally clear answer and immediately determined who was who.

Who was called Screw?