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?
Catherine asked Jennifer to multiply a certain number by 4 and then add 15 to the result. However, Jennifer multiplied the number by 15 and then added 4 to the result, but the answer was still correct. What was the original number?
In a bookcase, there are four volumes of the collected works of Astrid Lindgren, with each volume containing 200 pages. A worm who lives on this bookshelf has gnawed its way from the first page of the first volume to the last page of the fourth volume. Through how many pages has the worm gnawed its way through?
Michael thinks of a number no less than \(1\) and no greater than \(1000\). Victoria is only allowed to ask questions to which Michael can answer “yes” or “no” (Michael always tells the truth). Can Victoria figure out which number Michael thought of by asking \(10\) questions?
Can the equality \(K \times O \times T = U \times W \times E \times N \times H \times Y\) be true if the numbers from 1 to 9 are substituted for letters instead of the letters? Different letters correspond to different numbers.
Deep in a forest there is a small town of talking animals. Elephant, Crocodile, Rabbit, Monkey, Bear, Heron and Fox are friends. They each have a landline telephone and each two telephones are connected by a wire. How many wires were required?
Liz is 8 years older than Natasha. Two years ago Liz’s age was 3 times greater than Natasha’s. How old is Liz?
When Gulliver came to Lilliput, he found that there all things were exactly 12 times shorter than in his homeland. Can you say how many Lilliputian matchboxes fit into one of Gulliver’s matchboxes?
The parliament of a certain country has two houses with an equal number of members. In order to make a decision on an important issue all the members voted and there were no abstentions. When the chairman announced that the decision had been taken with a 23-vote advantage, the opposition leader declared that the results had been rigged. How did he know it?
Find numbers equal to twice the sum of their digits.