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Card Trick 2

Can you explain how this card trick works?

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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?

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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?

Tinker, Tailor

Stage: 3 Short Challenge Level: Challenge Level:1


Bilbo and Frodo are essentially counting 1 through 8 and then going round again (with Tinker = 1, Tailor = 2, etc.). So if Bilbo finished on Sailor = 4 and Frodo finished on Poor Man = 6, then together they would reach $4+6=10$. But 10 is 2 after 8, and 2 = Tailor.

This problem is taken from the UKMT Mathematical Challenges.