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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?

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Tic Tac Toe

Age 11 to 14 Challenge Level:

We received only one correct solution to this problem.

There are only 49 winning lines, which no doubt many of you will find hard to believe. Duplication of lines obviously helped muddy the approaches that were used with this problem.

Laura of West Flegg GM Middle School used an approach which classified the type of winning line possible with accompanying sketches :

9 vertical lines, 18 horizontal and 22 diagonal lines.
(Of the diagonal lines 6 go from front to back, 6 go from left to right, 6 go from top to bottom while four lines connect the 8 corner cells.)

a total of 49 lines
(27 of length 1, 18 of length Root 2 and 4 of length Root 3)