Imagine a right triangle (formerly called a rectangled triangle). One side adjacent to the right angle is twice as long as the other. You will not find it very difficult to construct a square from 4 of these triangles.
But is it possible to construct a square from 5 of these triangles? And from 6? From 7?
These problems are derived from ‘doordenkertje’ 12 in the November 1969 issue of ‘Pythagoras’, a Dutch magazine in recreational mathematics. You will need some elementary geometry knowledge to solve this problem.
You can check your solution here
Which code belongs at the question mark?
If you wish, you can peek at a hint
I have long suspected that there is a strong connection between mathematics and puzzles. Proving such a relation according to the scientific standards is of course another matter. It was nice to read that a study by the University of Chicago found that puzzle play helps boost Learning Math-Related skills in children between ages 2 and 4.
For the Puzzle-Olympics, the International Brain Olympics Committee is purchasing gold, silver and bronze medals. In the medal shop, the bronze, silver and gold medals each have their own prize. Unfortunately for the procurement officer, only sets have price labels.
What is the prize of the fourth set?
If you are puzzled, we have a hint for you.
Cubes are wonderful things. With six side surfaces, eight vertices and 12 edges, they are highly symmetrical. There are 11 ways to flatten a cube into a plane by cutting the edges. Here are 6 of the 11 ways:
Can you tell which cube is different? You can ignore the orientation of the letters – they are merely for identification. The symbols have been added for those readers who are colourblind.
If you are puzzled, we have a solution for you.
Did you know?
The subiculum plays a role in spatial navigation, mnemonic (symbol) processing. You probably already understood that this puzzle challenges the 3D representation facilities of your brain.