1. You have twelve coins. You know one is a dud and is a different weight from the others. You have a balance, but no weights. What is the least number of weightings you need to find the dud and determine whether it is light or heavy?

2. A knock out tennis tournament has entries from 137 players. The organiser is not sure how to arrange the number of players, so he pairs off as many entrants as he can and gives one bye (that is, one person goes through to the next round without having to play). He repeats this every round. How many matches are played from round one to the final??

3. You have 6 matchsticks. Arrange them so they form 4 equilateral triangles.

4. A girl goes into a supermarket and buys 4 items. Using a calculator she multiplies the prices (in pounds) instead of adding them. At the checkout she says, “so that’s £7.11?” The checkout man adds the prices correctly and agrees. What were the prices of the 4 items?

5. Lay out all of the dominos flat and upside down. Turn a domino over and record the total number of spots. Do this 50 times and record your results in a table. Which number are you most likely to turn up??