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2023 BIMC keystage2-EMIC team Question 4

xIMC · 2023 BIMC keystage2-EMIC team

Question 4

There are 8 circles on a rectangular board as shown in the diagram below. The distances between any pair of adjacent circles, horizontally or vertically, are all equal. Boris wants to colour some circles in red. How many ways can Boris colour some of the circles so that the resulting board has no line of symmetry?

Question illustration

Paper instruction: Give a full solution.