Earlier today I shared with you three math problems from a competition for Hungarian schoolchildren, who were jokingly referred to as Martians due to their exceptional intelligence back in the mid-twentieth century. Let’s revisit the puzzles and their solutions.
1. Curb your enthusiasm (Ages 13/14)
On an island, there are residents who are either half-hearted or enthusiastic. A visitor asked 10 residents about the number of enthusiastic inhabitants in their group and received the following answers: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. By considering the constraints that half-hearted individuals can’t overstate the number and enthusiastic individuals can’t understate it, we deduce that there are 6 enthusiastic inhabitants.
2. Edgy logo (Ages 11/12)
The challenge is to create a 2D logo using equilateral triangles and squares with a side length of 1 cm, without any overlap. The task is to make a logo with a perimeter of 13 cm. It is impossible to achieve this with only squares as all perimeter values would be even.
3. Axehead tiles (Ages 15/16)
The tiles have quarter circles as edges, and the area of a tile, with a height of 12 cm, is determined to be 72 cm². By dissecting the tile and rearranging the parts, we find the area to be 72 cm².
These puzzles are from the Dürer Competition, a Hungarian math contest for 10 to 18-year-olds. For more engaging puzzles, you can explore “Mathematical Explorations for Young Minds.”
If you enjoyed these challenges, you may be interested in “Think Twice: Solve the Puzzles That (Almost) Everyone Gets Wrong,” a book that presents counter-intuitive conundrums to test your thinking skills. You can order your copy to support the Guardian and Observer at guardianbookshop.com.
I have been sharing puzzles here since 2015 and I am always open to new puzzle suggestions. Feel free to email me with your ideas.
