Can Jennifer draw an octagon and a line passing through two of its vertices in such a way that this line cuts a 10-gon from it?
(a) Can one fit 4 letters “T” (see the picture below) in a \(6\times6\) square box?
We do not allow any overlappings to occur.
(b) Can we fit them in a square with smaller side length?
After having lots of practice with cutting different hexagons with a single cut Jennifer thinks she found a special one. She found a hexagon which cannot be cut into two quadrilaterals. Provide an example of such a hexagon.
Some countries write dates in the order month–day–year, while others use day–month–year. In a non-leap year, how many dates can be understood without knowing which of the two systems is being used?
The cells of a \(15 \times 15\) square table are painted red, blue and green. Prove that there are two lines which at least have the same number of cells of one colour.
In a bookcase, there are four volumes of the collected works of Astrid Lindgren, with each volume containing 200 pages. A worm who lives on this bookshelf has gnawed its way from the first page of the first volume to the last page of the fourth volume. Through how many pages has the worm gnawed its way through?
Can the equality \(K \times O \times T = U \times W \times E \times N \times H \times Y\) be true if the numbers from 1 to 9 are substituted for the letters? Different letters correspond to different numbers.
Liz is 8 years older than Natasha. Two years ago Liz’s age was 3 times greater than Natasha’s. How old is Liz?
A pedestrian walked along six streets of one city, passing each street exactly twice, but could not get around them, having passed each one only once. Could this be?
In two purses lie two coins, and one purse has twice as many coins as the other. How can this be?