Hungary acquired a reputation for brilliance in maths and physics in the middle of last century, thanks to scientists like John von Neumann, Edward Teller and Eugene Wigner.
The stellar cohort become known as the Martians. The Hungarians, so the joke went, were evidence that superior alien intelligence had already landed on Earth. Even their language was impenetrable.
Hungary has always led in science outreach too, starting the world’s first maths competition for teenagers in 1894. Today’s puzzles come from a more recent Hungarian math competition, about which more below. I’ve included the age level the problems are aimed at, just so you know.
Are you as smart as an 11-year-old Martian?
1. Curb your enthusiasm (Ages 13/14)
On an island, every resident is either half-hearted or enthusiastic. A visitor from a distant land was invited for dinner by a group of 10 residents. After dinner, the visitor asked all 10 members of the group about the number of enthusiastic inhabitants within their group.
She received the following answers: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Knowing that the answers of the half-hearted individuals cannot be more than the actual answer, and the answers of the enthusiastic individuals cannot be less than the actual number, determine the number of enthusiastic inhabitants within the group.
2. Edgy logo (Ages 11/12)
The task here is to design a 2D logo using only equilateral triangles and squares, each with a side length of 1 cm. The triangles and squares must be glued together along their entire sides without any overlap.
Make a logo with a perimeter of 13 cm from the following shapes or prove it is impossible:
a) A single triangle and some squares
b) The same number of squares and triangles.
c) Only triangles.
d) Only squares.
3. Axehead tiles (Ages 15/16)
The edges of these identical tiles are quarter circles, and their centres are the points marked. Determine the area of a tile, measured in cm2, given that the height of a standing tile is 12cm.
I’ll be back at 5pm UK with the solutions. Meanwhile, PLEASE NO SPOILERS. Please instead discuss your favourite Hungarians.
The puzzles are taken from the Dürer Competition, a maths contest for 10 to 18 year olds that has been running in Hungary since 2007. It was founded by a group of first year students at Budapest’s ELTE university, who wanted to create a fun competition that they would have enjoyed as children; less formal (and less hard) than more traditional competitions like olympiads. The competition has brought new energy to maths outreach in Hungary, and a selection of its questions are just out in a book, Mathematical Explorations for Young Minds.
I’m the author of Think Twice: Solve the Puzzles That (Almost) Everyone Gets Wrong, a collection of counter-intuitive conundrums that make you think about thinking – while enjoying the pleasure of being misled. The questions are not ‘trick’ questions; instead, they reveal our biases and flawed reasoning.
Think Twice: Solve the Simple Puzzles (Almost) Everyone Gets Wrong. To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply. (In the US, the book is called Puzzle Me Twice.)
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.