Problem 10 · 1997 AJHSME
Medium
Geometry & Measurement
grid-counting
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Answer: C — 7/12.
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Hint 1 of 2
The stripes are equal width, so impose a grid where one stripe = one cell wide. The figure spans 6 widths, so overlay a 6 × 6 grid and the messy picture becomes pure counting.
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Hint 2 of 2
Turning a 'to scale' shaded-region picture into a unit grid converts area into countable squares — the standard move for these.
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Approach: overlay a unit grid and count cells
- Equal stripe widths let you tile the square with a 6 × 6 grid (36 unit cells), so each black L-shaped stripe is a whole number of cells.
- Counting the three black L's from inside out gives 3, 7, and 11 cells — total 3 + 7 + 11 = 21 shaded.
- Shaded fraction = 21/36 = 7/12.
- Nice pattern: the black L's grow 3, 7, 11 — jumping by 4 each time, since each larger L wraps an extra cell along two arms. Spotting the +4 rhythm guards against a miscount.
- You'll see it again: 'drawn to scale, equal widths' is a hint to grid it; counting cells beats fighting with areas.
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