1 Coins in the dark

On a table in a dark room there are 100 coins. Exactly 10 are heads-up; the rest are tails-up. You may not look at or feel which is which. You may turn coins over. Split the coins into two piles so that the two piles have the same number of heads-up coins.

2 Cube cut

Hang a cube from one of its corners. Pass a plane through it horizontally, at the height of the cube’s centre. What shape is the cross section?

3 Ten liars

Ten people are in a room. Each one either always tells the truth or always lies.

1. Person 1 says, “There is at least one liar here.”
2. Person 2 says, “There are at least two liars here.”
3. …
4. Person 10 says, “There are at least ten liars here.”

How many liars are there?

4 Two liars

A fork in the road has one safe path and one unsafe path. Two people stand there. Each either always tells the truth or always lies, and you do not know who is which. One of them says, “The other one lies.” You may ask the other person a single yes-or-no question. What do you ask to find out which path is safe?

5 Vampire hunting

A vampire sleeps in one of six caskets in a row. Each night he moves to a casket next to the one he used the night before. Each day you may open a single casket. Give a strategy for choosing which casket to open which is guaranteed to catch him.

6 Calendar cubes

A desk calendar shows the day of the month with two cubes, which you may place in either order. The faces of the cubes must be able to form every date from 00 through 31. What digits go on the six faces of each cube?