Can you cover a \(10 \times 10\) square with \(1 \times 4\) rectangles?
Two opposite corners were removed from an \(8 \times 8\) chessboard. Can you cover this chessboard with \(1 \times 2\) rectangular blocks?
One small square of a \(10 \times 10\) square was removed. Can you cover the rest of it with 3-square \(L\)-shaped blocks?
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?
Can you cover a \(13 \times 13\) square using two types of blocks: \(2 \times 2\) squares and \(3 \times 3\) squares?
Deep in a forest there is a small town of talking animals. Elephant, Crocodile, Rabbit, Monkey, Bear, Heron and Fox are friends. They each have a landline telephone and each two telephones are connected by a wire. How many wires were required?
Prove that the medians of the triangle \(ABC\) intersect at one point and that point divides the medians in a ratio of \(2: 1\), counting from the vertex.
A ream of squared paper is shaded in two colours. Prove that there are two horizontal and two vertical lines, the points of intersection of which are shaded in the same colour.
A unit square contains 51 points. Prove that it is always possible to cover three of them with a circle of radius \(\frac{1}{7}\).
Fill an ordinary chessboard with the tiles shown in the figure.