Problem 10 · 2014 Math Kangaroo
Medium
Geometry & Measurement
areacareful-counting
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Answer: B
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Hint 1 of 2
Measure area in half-cell triangles: each small square is two triangles.
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Hint 2 of 2
Count how many black triangles and white triangles are already there, then see what the missing square must add to make the two totals equal.
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Approach: count black vs white half-cells and balance with the missing square
- Treat each small square as two triangles and count the black triangles and the white triangles already drawn in the eight filled squares.
- There are more white triangles than black so far, by exactly two triangles — one whole square's worth.
- So the missing square must be entirely black to even the totals out.
- That is the all-black square, choice B.
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