Break a leg

You stand before a building with a hundred floors holding two cats. When a cat is dropped from a certain height (which is the same for all cats) it breaks a leg. Your task is to determine the highest floor from which a cat will not break a leg. A healthy cat will – as everyone knows – always land on its feet. A cat with a broken leg however will avoid landing on its feet (thus a cat with a broken leg is useless in finding out whether a drop will break its leg or not).

How many times do you need to drop a cat (at most)?

Annoying aritmethics

Using the numbers (yes, numbers not digits) 1, 5, 6 and 7 each exactly once and the functions addition, subtraction, multiplication, division and negation as many times as you like can you get 21?

The drunken zoo keeper

First of all: Sorry for the late update.

A zoo keeper likes to play an odd game when he gets drunk (which is quite often). What he does is he takes all the turtles he can find and arranges them in a line. The turtles being scared by this hide in their shells, and thus doesn’t walk away while the game is played.

After lining up the turtles, the zoo keeper goes back to the front of the line and starts flipping every second turtle over. When he is done with that he goes back to the front and flips every third turtle and so on until the last time he flips the last turtle. When he is done with this he usually falls asleep from exhaustion (the distance he walks is after all quadratic in the number of turtles). While he sleeps the turtles that are turning feet down walks away as soon as they sense that all the flipping is over.

As mentioned the zoo keeper plays this game frequently and he can not help noticing a pattern in the number of turtles that leave while he sleeps. What is the pattern he sees? Or in other words; as a function of the total number of turtles, how many end up with their feet on the ground.

The eccentric coin collector

A coin collector who hasn’t heard of solitaire plays a homemade coin game to pass some of the time. The game goes like this: Place a number of coins in a rectangle all facing tails-up. Now you must alternately pick a column and a row and flip all the coins in that column or row. The goal is to have all the coins facing heads-up. Below is shown the course of a won game with 4×4 coins.

The question is: is it always possible to win this game no matter how many coins there are?

Man eating physicists

A tribe of man eating physicists have caught a hundred computer scientists and are about to devour them. However the captives are given a riddle that, if solved, will save their lives; The computer scientists are put in a line so that the last one can see the other ninety-nine in front of him, the second to last can see ninety-eight, etc., and the first one can see none of his friends. Then a fez – red, green or blue – is placed on the head of each computer scientist. If he can guess the color of his fez, he will be let go. The physicists ask the last computer scientist the color of his fez first, then the second to last, and so on.

Now, computer scientist are smart people, so they have agreed beforehand on how to answer. How many computer scientists are guaranteed to go free?

Oddball

You are given twelve balls and a scale. The balls all weigh the same except one that is either heavier or lighter than the rest.

Using the scale no more than three times, can you determine which ball is the “odd” one, as well as whether it’s heavier or lighter than the others?

“On the surface area of modern art”

Here is a piece of modern art:

Assuming that the piece is rectangular and the lines are straight and go from the corners, which area is bigger – the red or the blue?

Coins in the dark

In a dark room lie a hundred pennies. Ninety are facing heads-up and the remaining ten are facing tails-up. You can’t feel which are which.

Can you arrange the pennies into two piles each containing the same number of tails?

A peculiar kind of checkers

We need a checkers board, a checker and some pieces of paper cut into angles that cover up exactly three squares on the checkers board. Like this:

Put the checker somewhere on the board at random. Now the goal is to cover the whole board with the pieces of paper (without any of them overlapping or hanging outside the board). Like so:

Now imagine that your checkers board is not eight times eight squares but n times n squares where n is a power of two. Place the checker somewhere at random.

Is it always possible to cover the whole board with the angle cut pieces of paper?

Reboot

This blog has been lying dormant for some time. I guess it’s due to me not really having a good idea of what to write on it. But now I’ve got it: Riddles. I will try to post a new riddle every week. I haven’t decided whether to post solutions as well or not. We’ll see about that later on.

Since I’m a computer scientist with a weakness for mathematics,  the riddles will probably be mostly (or exclusively) mathematical in nature.

I think riddles (mathematical or not) is a great tool for keeping your mind open and flexible. Oftentimes the solution to a riddle is ridiculously obvious once you see it,  yet it can be very hard to find. Many real problems have this property – especially in academia. In other words: You won’t make it with hard work alone. And that is why one should care for riddles.

I hope you will enjoy these riddles as much as I do.