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coloured counters

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skilliyay | 06:41 Tue 13th Jun 2006 | Quizzes & Puzzles
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Phil has a 2x2 grid and a bag of different coloured counters, he can put one counter in each of the four squares. He calculates that he can make 2401 different grids with his counters.


assuming he has at least four of each coloured counter, how many different grids could he make with one extra colour?

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Suppose he has x different colours available. It is implicit in the question that he can repeat colours if he wishes.


That means he has x choices for each of the four squares. That is, he has a total of x times x times x times x choices. This x to the power 4.


2401 is 7 to the power 4. Therefore he started with 7 colours.


With 8 colours he could make 8 to the power 4 different grids.


8 to the power 4 is 4096

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