1. Alice and Bert are at a fairground and play on the coconut shy. They each get a total of 10 balls to throw, in 2 rounds. In the first round, Alice throws 9 balls and successfully hits a coconut 56% of the time. Bert throws 4 coconuts and has a success rate of only 50%.

    In the second round, Alice throws the only balls she has left, and hits a coconut! Bert throws 6 balls, but is only successful 83% of the time. The winner is the person who manages to hit the most coconuts.

    Who wins the game?

  2. I need to get a fox, a hen and some corn across a river. I have a boat in which I can only take one of these with me at once. I must not leave the fox and the hen together on either side of the river, or the fox will eat the hen. I must not leave the hen and the corn together on either side of the river, or the hen will eat the corn. What is the minimum number of times that I need to cross the river to get all three things across?

  3. Without using a calculator calculate 5840 X 4730

  4. What is the lowest common multiple of 24 and 39?

  5. I start with a pint glass full of lemonade. I drink half of it and give it to you. You then drink half of what is left and give it back to me. I then drink half of what is left, and pass it back. We keep drinking half of the remaining lemonade then passing it across until there is a negligible amount od drink left.

    In total, what proportion of the pint did I drink?

  6. There are 4 people called A,B, C and D. Three of them always tell the truth. One of them always lies.

    Person A says that person D is telling the truth.

    Person B says  that person C is lying

    Person C says ‘I am telling the truth’

    Person D says that person B is lying

    Which person is the lier?

  7. I have two identical pint glasses. One contains half a pint of orange juice and the other contains half a pint of apple juice. I have a small calibrated measuring spoon. I take 20 ml from the orange glass, put it in the apple glass and stir well to ensure thorough mixing. I then take 20 ml of the apple/orange mixture, put it in the orange glass and mix it in. Is there more apple in the orange or orange in the apple? Or is there the same amount of orange in the apple juice glass as there is apple in the orange juice glass?

  8. There are three playing cards face up in a row. They all have different values and different suits.

    The diamond is to the right of the spade.

    The 10 is to the left of the ace.

    The 2 is between the heart and the diamond. What is the left-most card?

  9. Three male prisoners are sitting in a line one behind another. They are shown 2 red and 3 green hats, and a hat on is put on each man’s head so that each cannot see his own hat, but can see the hats on the other prisoners ahead of him. As a result, the front prisoner cannot see anything; the middle prisoner can see the front prisoner’s hat and the back prisoner can see the hats on both the front and middle prisoner.

    They are told that they will be set free if any of them can get his own hat colour right without communicating with any other prisoner.

    The front prisoner becomes aware that both the back and middle prisoners have chosen to remain silent. Assuming that all the prisoners make optimal logical decisions throughout the challenge, what is the best action that can be taken by the front prisoner?

  10. Father Christmas needs to arrange his eight reindeer in four rows of two. However, he needs to observe the following rules about the reindeer:

    • Blitzen must always be on the left-hand side but not in the rear row
    • Comet and Cupid must be in either of the first two rows, but not necessarily in the same row
    • Dancer must always be directly behind Donner
    • Prancer must always be ahead of Dasher but never on the same side, and never next to Comet or Cupid
    • Vixen must be as far away from Blitzen as possible and not on the same side

    From left to right, which two reindeer make up the rear row?