Problem 23 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
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Elena wants to write the numbers from 1 to 9 in the squares shown. The arrows always point from a smaller number to a larger one. She has already written 5 and 7. Which number should she write instead of the question mark?
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Answer: D — 6
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Hint 1 of 3
Every arrow goes from a smaller number to a larger one, so the box where all arrows point in must hold a big number and the box where all arrows point out must hold a small one.
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Hint 2 of 3
Follow the arrow trails out from the boxes that already show 5 and 7, always stepping up to a bigger number.
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Hint 3 of 3
Work out which numbers are still allowed in the ? box after the small numbers are forced into the lower boxes.
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Approach: use 'arrows go small to large' to squeeze out which number fits the ? box
- The top-left box gets an arrow in from the 7, so it must be bigger than 7, which means it is 8, and the box it points to is the biggest of all, 9.
- Following the arrows down and to the left, every box on the bottom-right side has to be smaller than 5, so 1, 2, 3 and 4 are all used up down there.
- That leaves only 6 free for the ? box (8 and 9 are taken by the top, and 5 and 7 are already placed).
- So she writes 6 for the question mark (D).
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