Problem 22 · 2015 Math Kangaroo
Stretch
Geometry & Measurement
square-areacareful-counting
In this square there are 9 dots. The distance between the points is always the same. You can draw a square by joining 4 points. How many different sizes can such squares have?
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Answer: D — 3
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Hint 1 of 2
Squares can sit straight on the dots, but they can also be tilted like a diamond.
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Hint 2 of 2
Hunt for a tiny straight square, a big straight square, and one slanted square.
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Approach: find every square size, straight ones and the tilted one
- On the 3-by-3 dots you can make a tiny straight square (1 step on each side) and a big straight square (2 steps on each side).
- You can also make a slanted square shaped like a diamond, joining the four middle dots of the edges.
- That is three squares of three different sizes.
- The answer is 3.
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