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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

Here are the instructions to a second card trick. This is also mathematical. Try and explain how it works.

Volunteer selects any three cards and places them face down on the table.

Volunteer then shuffles the pack of cards and returns them to me.

You are going to find a card in this pack which depends on the three cards you have already chosen. I am going to try and predict what card that will be. I am not going to alter the order of the cards, I am just going to remove a card which points to the card you will find.

Check the fourth from bottom card and remove the card of the same numerical value and colour and place it face down on the table.

Volunteer turns over each of the three cards in turn and counts onto 15 for each one. Remove the counted out cards each time. (Jack =11 Queen =12 King =13)

The numbers of the three cards are added, and that number of cards is counted out, the last one being kept.

Turn over that card and the predicting card.