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2009 Math Kangaroo

Problem 24

Problem 24 · 2009 Math Kangaroo Stretch
Logic & Word Problems caseworkgrid

We want to colour each square in the grid with one of the colours A, B, C and D so that neighbouring squares always have different colours. (Squares that share a corner also count as neighbouring.) Some squares are already coloured. Which colour(s) could the grey square be?

Figure for Math Kangaroo 2009 Problem 24
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Answer: A — A
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Hint 1 of 2
Neighbours include diagonal touches, so the grey square clashes with every square around its corner.
Still stuck? Show hint 2 →
Hint 2 of 2
List the colours already used by all squares touching the grey one; whatever is left is the answer.
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Approach: eliminate neighbour colours
  1. The grey square touches several painted squares, including diagonally.
  2. Those neighbours already use the colours B, C and D.
  3. The only colour left that differs from every neighbour is A.
  4. So the grey square must be A.
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