How can one measure out 15 minutes, using an hourglass of 7 minutes and 11 minutes?
Two boys play the following game: they take turns placing rooks on a chessboard. The one who wins is the one whose last move leaves all the board cells filled. Who wins if both try to play with the best possible strategy?
A traveller who came to the planet hired a local as a guide. They went for a walk and saw another alien. The traveller sent the guide to find out to whether this native is a liar or truth teller. The guide returned and said: “The native says that they are a truth teller.” Who was the guide: a liar or a truth teller?
In a basket there are 13 apples. There are scales, with which you can find out the total weight of any two apples. Think of a way to find out from 8 weighings the total weight of all the apples.
On the board the number 1 is written. Two players in turn add any number from 1 to 5 to the number on the board and write down the total instead. The player who first makes the number thirty on the board wins. Specify a winning strategy for the second player.
There are two stacks of coins on a table: in one of them there are 30 coins, and in the other – 20. You can take any number of coins from one stack per move. The player who cannot make a move is the one that loses. Which player wins with the correct strategy?
Three people are talking at dinner: Greyson, Blackburne and Reddick. The black-haired person told Greyson: “It is curious that one of us is grey-haired, the other is black-haired, and the third is red-haired, but no one has hair colour that matches their surname.” What colour hair does each of the men chatting have?
A journalist came to a company which had \(N\) people. He knows that this company has a person \(Z\), who knows all the other members of the company, but nobody knows him. A journalist can address each member of the company with the question: “Do you know such and such?” Find the smallest number of questions sufficient to surely find \(Z\). (Everyone answers the questions truthfully. One person can be asked more than one question.)
In the government of the planet of liars and truth tellers there are \(101\) ministers. In order to reduce the budget, it was decided to reduce the number of ministers by \(1.\) But each of the ministers said that if they were to be removed from the government, then the majority of the remaining ministers would be liars. How many truth tellers and how many liars are there in the government?
One and a half diggers dig for a half hour and end up having dug half a pit. How many pits will two diggers dig in two hours?