# Can you solve it? The playful genius of Hungarian puzzles

Logic puzzles in three dimensions

UPDATE: To read the solutions click here

When it comes to the world of mathematical puzzles, Hungary is a superpower. Not just because of the Rubik’s cube, the iconic toy invented by Ernő Rubik in 1974, but also because of its long history of maths outreach.

In 1894, Hungary staged the world’s first maths competition for teenagers, four decades before one was held anywhere else. 1894 also saw the launch of KöMaL, a Hungarian maths journal for secondary school pupils full of problems and tips on how to solve them. Both the competition and the journal have been running continuously since then, with only brief hiatuses during the two world wars.

This emphasis on developing young talent means that Hungarians are always coming up with puzzles designed to stimulate a love of mathematics. (It also explains why Hungary arguably produces, per capita, more top mathematicians than any other country.)

I asked Béla Bajnok, a Hungarian who is now director of American Mathematics Competitions, a series of competitions involving 300,000 students in the US, whether he knew of any puzzles that originated in Hungary. The first thing he said that came to mind was the ‘3-D logic puzzle’, a type of logic puzzle in which you work out the solution in a three dimensional box, rather than (as is the case with the standard version) in a two-dimensional grid. He said he had never seen this type of puzzle outside Hungary.

Below are two examples he created. You could solve these using an extended two dimensional grid. It’s more in the spirit of the question, however, to draw a three-dimensional one, like you are looking at three sides of a Rubik’s Cube.

1. Date night

Andy, Bill, Chris, and Daniel are out tonight with their dates, Emily, Fran, Gina, and Huong. We have the following information.

1. Andy will go to the opera

2. Bill will spend the evening with Emily,

3. Chris would not want to go out with Gina,

4. Fran will see a movie

5. Gina will attend a workshop.

We also know that one couple will see an art exhibit. Who will go out with whom, and what will they do?

2. Condo conundrum

When Mr and Mrs Verona opened the door to their condominium at 11am this morning, they saw a terrible sight: their beautiful home had been burgled. They called the police, who came over immediately. The upcoming investigation revealed the following.

1. There are six condominiums in the building, numbered 1 to 6, the Veronas owned #4.

2. The Veronas left their home at 6pm last night.

3. The night guard of the building, Mr. Safe, works from 6pm till 10am.

4. There were six visitors in the building during last night: Mr A. Bream, Miss F. Green, Mr R. Hill, Dr T. Smith, Miss T. Taylor, and Mr Z. White. They all visited one of the six condominiums, each a different one, some time between 6pm and midnight. Mr. Safe could not recall, however, who visited which place; but he was sure that none of them stayed longer than an hour. Furthermore, they all stayed during different hours; the first one between 6pm and 7pm, the second between 7pm and 8pm, and so on.

5. Mr Bream was at a huge party at the country club. He arrived there at 8pm and stayed till midnight.

6. Miss Green was also at the country club; she arrived at 9pm and left with Mr Bream.

7. Mr Hill could not provide any credible alibi for the night before.

8. Miss Taylor was at her home watering her front yard between 7.45pm and 9pm. Several of her neighbors saw her.

9. Mr White was at the party at the country club. He arrived at 7pm and left at 10pm but, surprisingly, he came back again at 11pm and stayed till after midnight.

10. No one could enter the condominium without going through the lobby where Mr. Safe was stationed.

11. None of Dr. Smith’s, Miss Taylor’s, or Mr White’s fingerprints were found in condo #5.

12. Dr Smith could not have visited condos #1, #3, or #6.

13. Miss Green couldn’t have visited condos #3 and #6.

14. Mr Safe recalled that shortly before 8pm a visitor left either condo #1 or #4.

15. Nobody entered condos #5 and #6 before 7pm.

16. A visitor arrived at 8pm, and entered condo #1, #3, or #6.

17. Nobody visited condos #2, #3, and #6 between 10pm and 11pm.

Well, these were all the clues that the police investigation revealed during the first day of the investigation. Can they solve this terrible crime without further information?

I’ll be back at 5pm UK time with the solutions.

PLEASE NO SPOILERS Instead discuss your favourite Hungarians.

UPDATE: To read the solutions click here.

Thanks to Béla Bajnok for today’s puzzles. He is is Professor of Mathematics at Gettysburg College in Pennsylvania and director of American Mathematics Competitions.

I set a puzzle here every two weeks on a Monday. I’m also the author of several books of popular science, most recently The Language Lover’s Puzzle Book, just out in paperback.

Finally, it’s Maths Week England next week (from November 8). Parents and teachers, you can register your school here.

Alex Bellos

The Guardian

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