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Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Cube Paths

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

How Many Dice?

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?

Card Trick 2

Age 11 to 14
Challenge Level

You may have found that this trick does not work if the fourth card from the bottom is the same numerical value and colour as one of the 3 chosen cards or as the first, second or third card from the bottom, a probability of 6/45. When the 'magician' looks at the cards and sees that this has happened the best thing is to carry on with the trick but first to say that the cards should be shuffled again and give some convincing reason!


The card which the volunteer keeps will always be the fourth card from the bottom of the pack which has the same numerical value and colour as the predicting card. This is because, whatever 3 cards are selected by the volunteer, with these 3 cards and the predicting card, 4 cards are removed from the pack. Then 45 cards are counted out, and this leaves the last 3 cards to make up 52 altogether. Suppose the 3 cards selected have values x , y and z then the number of cards counted out is (15 - x ) + (15 - y ) + (15 - z ) + x + y + z = 45.

Correct solutions were sent in by:

Sarah - Archbishop Sancroft High School