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There are three piles of rocks: in the first pile there are 10 rocks, 15 in the second pile and 20 in the third pile. In this game (with two players), in one turn a player is allowed to divide one of the piles into two smaller piles. The loser is the one who cannot make a move. Which player would be the winner?

In the first pile there are 100 sweets and in the second there are 200. Consider the game with two players where: in one turn a player can take any amount of sweets from one of the piles. The winner is the one who takes the last sweet. Which player would win by using the correct strategy?

The grandad is twice as strong as the grandma, the grandma is three times stronger than the granddaughter, the granddaughter is four times stronger than the dog, the dog is five times stronger than the cat and the cat is six times stronger than the mouse. The grandad, the grandma, the granddaughter, the dog and the cat together with the mouse can pull out the pumpkin from the ground, which they cannot do without the mouse. How many mice should be summoned so that they can pull out the pumpkin themselves?

There are two hourglasses – one for 7 minutes and another for 11 minutes. An egg is boiled for 15 minutes. How can this time be measured with the help of the available hourglasses?

Two people had two square cakes. Each person made 2 straight cuts from edge to edge on their cake. After doing this, one person ended up with three pieces, and the other with four. How could this be?

How can you divide a pancake with three straight sections into 4, 5, 6, 7 parts?

What is the maximum number of pieces that a round pancake can be divided into with three straight cuts?

The best student in the class, Katie, and the second-best, Mike, tried to find the minimum 5-digit number which consists of different even numbers. Katie found her number correctly, but Mike was mistaken. However, it turned out that the difference between Katie and Mike’s numbers was less than 100. What are Katie and Mike’s numbers?