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Card Trick 2

Can you explain how this card trick works?

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?

Pairs

Age 11 to 14 Challenge Level:

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.

[This is an exercise for practice from the Hungarian KöMaL magazine, September 2000 issue. You'll find many other challenging problems in English on the KöMaL website.]