On 99 cards, write the numbers 1, 2, ..., 99, mix them, lay them out with their

Represent each of the numbers 1101 and –1101 as a) 2n + 1; b) 2n – 1; c) 2n +

‍ 2 .The product of any two odd numbers is odd, but the sum is even. Prove it. ‍

Prove that if the sum of two integers is odd, then the product of these numbers

The difference of two integers is multiplied by their product. Could you get thi

Twenty years ago, banknotes in denominations of 1, 3, 5, 10 and 25 rubles were i

Ev writes one whole number on the board, and Od writes another. If the product i

chips are placed in a row. It is allowed to swap places of any two chips that st

There are 100 people in the company. Three are on duty every night. Is it possib

Numbers from 1 to 10 are written in a row. Is it possible to place “+” and “–” s

Is it possible to erase one of the given a) 1992; b) 1993 integers so that the s

Is it possible to divide the natural numbers 1, 2, ..., 20, 21 into several grou

You are allowed to add one to any two numbers. Is it possible to make all number

On 99 cards, write the numbers 1, 2, ..., 99, mix them, lay them out with their

The vertices and centres of the faces are marked on the cube, and the diagonals

There is a king on a certain square of the chessboard. Two people take turns mov

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