A 2 x 2 grid Filled with Two Colors

Probability Level 2

A 2 x 2 grid is to have each cell filled with two different colors. How many distinct arrangements are there considering symmetries?


The answer is 6.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

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Does this approach extend to two colours on an n × n n \times n grid? Or more colours?

Chris Lewis - 4 months, 1 week ago

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Best way to answer this is to give you a link for a 3 x 3 grid with 5 colors. But the answer is yes, you just have to adopt Burnside's Lemma approach which is quite handy for handling large numbers. https://www.youtube.com/watch?v=D0d9bYZ_qDY&t=630s

A Former Brilliant Member - 4 months, 1 week ago

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