Hungary gained a reputation for brilliance in mathematics and physics in the middle of the last century, thanks to scientists such as John von Neumann, Edward Teller and Eugene Wigner.
The constellation became known as the Martians. The Hungarians, the joke went, were proof that superior alien intelligence had already landed on Earth. Even their language was impenetrable.
Hungary has always led in scientific outreach, initiation the world’s first math competition for teenagers in 1894. Today’s puzzles come from a more recent Hungarian math competition, more on that 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 country was invited to dinner by a group of 10 residents. After dinner, the visitor asked all 10 members of the group about the number of enthusiastic residents within their group.
She got 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 residents 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 along their entire sides without any overlap.
Make a logo with a circumference of 13 cm from the following shapes or prove it impossible:
a) A single triangle and a few squares
b) The same number of squares and triangles.
c) Only triangles.
d) Squares only.
3. Ax Head Tiles (ages 15/16)
The edges of these identical tiles are quarter circles, and their centers are the points marked. Determine the area of a tile, measured in cm2given that the height of a standing tile is 12cm.
I’ll be back at 5pm UK with the solutions. In the meantime, NO SPOILERS PLEASE. Please book your favorite Hungarians instead.
The puzzles are taken from the Dürer competitiona mathematics competition 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 harsh) than more traditional competitions such as Olympiads. The competition has brought new energy to maths outreach in Hungary, and a selection of its questions has just been published 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 counterintuitive puzzles that make you think about thinking—while enjoying the pleasure of being tricked. The questions are not ‘trick’ questions; instead, they reveal our biases and flawed reasoning.
Think twice: solve the simple puzzles (almost) all get wrong. To support the Guardian and Observer, order your copy from guardianbookshop.com. Delivery charges may apply. (In the US the book is called Puzzle Me Twice.)
I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.
