# Coloring a cube

In how many ways a cube can be colored with n different colors such that no 2 neighboring or adjacent faces are colored with same color?

Note by Abdullah Ahmed
1 year, 8 months ago

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## Comments

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I have solved it .

- 1 year, 7 months ago

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Great! How would you explain the approach?

Staff - 1 year, 7 months ago

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Isn't the formula 1/24(n^6+12n^3+3 n^4+8n^2)? I know it from Burnside's lemma. but in the question two adjacent sides are not colored with same color. so what is the general formula for it? @Calvin Lin

- 1 year, 8 months ago

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Staff - 1 year, 8 months ago

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