Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?

Can you decipher the two rows to find the hidden word?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

A donkey is behind another donkey
I'm behind that second donkey
But there is a whole nation behind me

It is a murder you can describe in a word.