Problem 10 · 2025 Math Kangaroo
Medium
Spatial & Visual Reasoning
grid
In the \(xy\) plane, some points in the range \(0 \le x \le 1\), \(0 \le y \le 1\) are coloured black. A point \((x\,|\,y)\) is coloured black if and only if the first decimal digit of both \(x\) and \(y\) after the decimal point is odd. What does the result look like?
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Answer: E
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Hint 1 of 2
List which first-decimal digits are odd for x, and the same for y.
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Hint 2 of 2
Odd first digit means x lies in [0.1,0.2)∪[0.3,0.4)∪…∪[0.9,1.0): five separated strips each way.
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Approach: intersect two sets of strips
- x has an odd first decimal in five disjoint strips; same for y.
- Black points form a 5×5 array of separated squares with gaps between them.
- That matches picture E.
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