Problem 10 · 2021 Math Kangaroo
Medium
Logic & Word Problems
caseworkcareful-counting
Sofie wants to pick 5 different shapes, taking exactly 1 shape from each box. Which shape must she pick from box 4?
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Answer: E
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Hint 1 of 2
Start with a box that holds only one shape Sofie still needs — that pick is forced, with no real choice.
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Hint 2 of 2
Cross off each shape as it gets used up, and see which single shape box 4 is left to give.
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Approach: use the forced choices to deduce what box 4 must give
- She needs 5 different shapes and one box can only offer the shapes drawn in it, so look for boxes where the pick is forced.
- Make those forced picks first and cross each chosen shape off the list.
- Once the other boxes have used up their shapes, box 4 is left with only one shape it can still supply — the one in option E.
- So from box 4 she must pick E.
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