Man alive, I’m burnin’ up on my brain.
She knows when I’m just teasin’
But it’s not likely in the season
To open up a passenger train.
- SILENT WEEKEND

Complete change of scenery today. I haven’t thought about puzzles for many years, but a recent post reminded me how much I like them. So I figured I’d dredge up a list I put together about 13 years ago and publish them here. You should be able to figure them all out over a beer without pen and paper. Seeing as I didn’t invent any of these myself, you’ll also probably be able to Google the answers if you’re the lazy, low-down cheating type. I’m not going to include the Monty Hall Problem as it starts too many fights. Credit to all the people that created these. I can’t remember where I found them all.

Problem #1: The Dangling Cube

Take a hollow glass cube, exactly half filled with a coloured liquid. If you place the cube flat on a table, the surface of the liquid, seen from above, makes a square. What two dimensional shape does the surface make if you dangle the cube from a piece of string attached to one of the corners?

Problem #2: The Mutilated Chess Board

You have an 8×8 square (say a chessboard), and 32 dominoes each exactly the same size as two squares. It is easy to cover the chessboard (64 squares) totally using the 32 dominoes. Now, you take away one domino, and cut off two opposite corners of the chessboard (a1 and h8 for the chessplayers). Now you have 31 dominoes and 62 squares. Is it still possible to cover the board. If so, how? If not, why not?

Problem #3: Fly on the Windshield

You have two trucks, 200km apart. Both trucks are heading towards each other at a constant speed of 50km/hour. On the windshield of one truck is a fly. He flys at a constant speed on 70km/hour from the windshield of one to the windshield of the other. When he hits a windshield, he turns instantly without slowing down. He continues to do this until the 2 trucks collide, squashing the poor fly. The question is, how far does the fly travel before getting squashed.

Problem #4: The Annoying Piles

You have 10 piles of 10 coins each. One pile consists of 10 counterfeit coins, while the other 9 piles consist of 10 real coins. A counterfeit coin weighs 11g, while a real coin weighs 10g. You have a scale (a normal kitchen scale, not a balance scale). What is the minimum number of weighings needed to determine which pile is counterfeit? You are, of course, extremely unlucky.

Problem #5: A Bridge Too Far

Four people want to cross a bridge. It is a very rickety bridge, so at most 2 people can cross at the same time. Unfortunately, it is also very dark, so in order to cross the bridge, the group must be holding a flashlight. The have only one. So, clearly 2 people must cross, 1 must come back, 2 go across etc. The four people take 1, 2, 5 and 10 minutes to cross the bridge. If 2 cross together, it takes the time of the slower to cross (if 2 and 5 crossed together, it would take 5 minutes). What is the minimum time needed for them all to cross.

I got asked this in interviews with Microsoft

Problem #6: Casanova’s Conundrum

One night at a bar, you meet 3 beautiful girls (or guys). You really want to sleep with all 3, but you only have two condoms. Each of the four people involved suspects all the others may have some kind of infectious disease. The question is, how do you arrange to have sex with all three without anyone having any chance of catching a disease from any other? (I’m sure there is another less graphic way to state the problem, but I like this one).

Problem #7: Annoying Algebra

Simplify the following multiplication:

(x-a)(x-b)(x-c) .... (x-y)(x-z).

That is, the are 26 terms in the multiplication. It does simplify considerably.

I got asked this in the South African Mathematics Olympiad where you had 30 mins per question.

Problem #8: The Mad Hatter

There are three black hats and two white hats. Three people, each with one hat, line up in a row like so: A B C. C can see both A and B, B can only see A, but A can’t see the other two. They can all hear each other. When person C is asked what colour hat he is wearing, he says he doesn’t know. When person B is asked what colour hat he is wearing, he doesn’t know either. When person A is asked, he knows and says it correctly. What colour hat is each person wearing?

Problem #9: The Mystery of the Missing Dollar

You and two friends decide to spend a night at a hotel. Rooms are 10 dollars per night per person. You each take 10 dollars (30 in total) and give it to the bellboy to go and order your rooms. When the bellboy gets to the reception,
he sees that there is a 3 for 25 dollars special. He pays with the 30 dollars, so gets 5 dollars change. As 5 dollars cannot easily be divied amoung 3 people, he give each person back 1 dollar, and keeps 2 for himself. Now, each person has paid 9 dollars (10 paid, 1 change), so they paid 27 dollars between them. The bellboy has 2 dollars. But 27+2=29, not 30. Where is the missing dollar?

Problem #10: The Gender Mind Bender

There is a town in a remote part of the world with a large population, and some strange habits. They all believe that one boy per family is enough. So, each couple continues to have children until they have their first boy. After this, they have no more children. Assuming that there is a 50 percent chance of each child being a boy, what will the ratio of boys to girls settle at after 20 generations? Why?