Problem 3 · 2015 Math Kangaroo
Easy
Logic & Word Problems
gridcareful-counting
Sam paints the 9 small squares in the shape either white, grey or black. What is the minimum number he must paint over so that no two squares sharing a side have the same colour?
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Answer: A — 2
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Hint 1 of 2
Find every pair of side-touching squares that currently share a colour; those are the trouble spots.
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Hint 2 of 2
Try to fix several clashes at once by changing a single well-chosen square, and count the fewest squares you must repaint.
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Approach: spot the colour clashes and repaint the fewest squares to break them all
- Scan the grid for neighbours that share a colour: the two grey squares touch, and the black squares touch.
- Changing two carefully chosen squares is enough to separate every same-colour pair, while one change still leaves a clash somewhere.
- So the minimum number Sam must paint over is 2.
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