Circle name: Circle Second

Lesson name: Lesson3

Starts at : 14.05.2020 09:00

Problems:

Two play a game on a chessboard 8 × 8. The player who makes the first move puts a knight on the board. Then they take turns moving it $($ according to the usual rules $)$, whilst you can not put the knight on a cell which he already visited. The loser is one who has nowhere to go. Who wins with the right strategy – the first player or his partner?

On the Island of Bad Luck there are only knights who always tell the truth, and liars who always lie. In the government of the island 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 he was to be removed from the government, then the majority of the remaining ministers would be liars. How many knights and how many liars are there in the government?

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.$)$