Problems

One small square of a $10\times 10$ square was removed. Can you cover the rest of it with 3-square $L$-shaped blocks?

There are real numbers written on each field of a $m\times n$ chessboard. Some of them are negative, some are positive. In one move we can multiply all the numbers in one column or row by $-1$. Is that always possible to obtain a chessboard where sums of numbers in each row and column are nonnegative?

A $7\times 7$ square was tiled using $1\times 3$ rectangular blocks. One of the squares has not been covered. Which one can it be?

Tom found a large, old clock face and put 12 sweets on the number 12. Then he started to play a game with himself. In each move he moves one sweet to the next number clockwise, and some other to the next number anticlockwise. Is it possible that after finite number of steps there is exactly 1 of the sweets on each number?

Can you cover a $13\times 13$ square using two types of blocks: $2\times 2$ squares and $3\times 3$ squares?

What time is it going to be in $2019$ hours from now?

What is a remainder of $1203\times 1203-1202\times 1205$ when divided by $12$?

Show that a perfect square can only have remainders 0 or 1 when divided by 4.

Convert 2000 seconds into minutes and seconds.

What is a remainder of $7780\times 7781\times 7782\times 7783$ when divided by $7$?