Problems

Solve the rebus \(AC \times CC \times K = 2002\) (different letters correspond to different integers and vice versa).

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)

Multiplication of numbers. Restore the following example of the multiplication of natural numbers if it is known that the sum of the digits of both factors is the same.

Restore the example of the multiplication.

Petya and Misha play such a game. Petya takes in each hand a coin: one – 10 pence, and the other – 15. After that, the contents of the left hand are multiplied by 4, 10, 12 or 26, and the contents of the right hand – by 7, 13, 21 or 35. Then Petya adds the two results and tells Misha the result. Can Misha, knowing this result, determine which hand – the right or left – contains the 10 pence coin?

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?

There are some weighing scales without weights and 3 identical in appearance coins, one of which is fake: it is lighter than a real coin (real coins are equal in weight). How many weighings are needed to determine a counterfeit coin?