Did you solve it? The playful genius of Hungarian puzzles

Earlier today I set you the following “three-dimensional” logic puzzles, a genre thought to have emerged decades ago in Hungary. (For more details about the Hungarian link here’s the story.) The idea is that the solution is mapped out on a three-dimensional grid.

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?

Solution

Here’s what I hoped you would do, which is to draw a 3D grid like the one below with the four alternatives on each axis. It’s as if you are looking at cube directly at a corner, showing three faces.

Once you have the grid, you go through the statements, inputting the information where you can. Statement 1 says that Andy goes to the opera. So you put a tick for Andy/opera, which appears on the right face of the cube. We need to assume that each date takes place in one location, so we can mark crosses in the cells Andy/movie, Andy/workshop and Andy/art, since we know he didn’t go to any of those places. Bill, Chris and Daniel don’t go to the opera, so the corresponding cells also gain an X.

Statement 2 says that Bill goes with Emily, so the top face will get a tick in the cell for Bill/Emily. If you continue in this way, you will fill up the grid with ticks and crosses. Each face will have four ticks only, and none of these ticks will share the same row or column. Finally, you will reach the conclusion that Andy and Huong attend the opera, Bill and Emily hang out at the art exhibit, Chris and Fran enjoy a movie, and Daniel and Gina go wild at the workshop.

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?

Solution

This time you need to draw a 6 x 6 x 6 cube grid, with the suspects along one axis, and the condos and the time slots along the two other axes. Gradually fill in the cells until you deduce that fishy old Bream did it.

I hope you enjoyed the puzzles. I’ll be back in two weeks.

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 always on the look-out for great puzzles. If you would like to suggest one, email me. I also give school talks about maths and puzzles (restrictions allowing). If your school is interested please get in touch.