Problem 24 · 2021 Math Kangaroo
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Logic & Word Problems
caseworklogic
Five kangaroos named A, B, C, D and E have one child each, named a, b, c, d and e, not necessarily in that order. In the first group photo shown exactly 2 of the children are standing next to their mothers. In the second group photo exactly 3 of the children are standing next to their mothers. Whose child is a?
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Answer: D — \(D\)
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Hint 1 of 2
Each child stands by a different kangaroo in the two photos, so a child can be correctly placed in at most one photo.
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Hint 2 of 2
Since 2 + 3 = 5 children, every child is correct in exactly one photo; sort out which assignment makes both counts work.
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Approach: match children to mothers by an exactly-one-photo argument
- In photo 1 the pairings are A-d, B-a, C-b, D-c, E-e (2 correct); in photo 2 they are A-b, B-e, C-d, D-a, E-c (3 correct).
- No child keeps the same partner across photos, so each child is correct in just one photo and all five split as 2 + 3.
- The only consistent bijection takes photo-1 pairs b–C, d–A and photo-2 pairs a–D, c–E, e–B, so a's mother is D.
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