- A party of four, consisting of two married couples, wants to share the same round table set for four people, so that each man sits next to his wife. How many different ways is this possible? The diagram shows one possible arrangement.
3. Which has the greatest volume? A 6m wide sphere, or a 5m wide cube? (Shown here to scale)
State the minimum number of moves that each of the following chess pieces, from its starting position on the board, (Row 1 or 2) requires to reach the other side of the board. (Row 8)
- At a recent visit to the reptile house at a local zoo, I counted a total of 27 heads and 70 feet. I was counting snakes, lizards and people. There were twice as many lizards as there were people.
(a) How many snakes were there?
(b) How many lizards were there?
(c) How many people were there?
6. A pole is placed in a lake so that half the pole is driven into the solid bottom of the lake, one third is covered by water, and the remaining 12 metres sticks up into the air.
How long is the pole?
“Two ducks in front of two other ducks, two ducks behind two other ducks and two ducks beside two other ducks”
- How many times do the hour and the minute hands of a clock cross each other in any twelve-hour period?
- Imagine you have two 12-sided dice with each face bearing a number from 1 to 12.
(a) When you roll two ordinary dice together, the most frequent score is seven. What score will come up most frequently when you repeatedly roll two of these 12 sided dice and add the two uppermost digits?
(b) What will be the chance of throwing a score of 24 with one throw of both dice?
- Alice, Bill and Charlie are all celebrating their birthday. Alice is twice Bill’s age and one year older than Charlie. Charlie was twice Bill’s age a year ago. How old are Alice, Charlie and Bill?