Maths Olympiad Prep

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Combinatorics Difficulty 2.2 Junior Find the answer

In a group of five friends, Amy is taller than Carla. Dan is shorter than Eric but taller than Bob. Eric is shorter than Carla. Who is the shortest?

A number or a short expression. Spacing and $ signs are ignored.

Solution

We use A,B,C,D,EA, B, C, D, E to represent Amy, Bob, Carla, Dan, and Eric, respectively. We use the greater than symbol (>)(>) to represent 'is taller than' and the less than symbol (<)(<) to represent 'is shorter than'. From the first bullet, A>CA > C. From the second bullet, D<ED < E and D>BD > B so E>D>BE > D > B. From the third bullet, E<CE < C or C>EC > E. Since A>CA > C and C>EC > E and E>D>BE > D > B, then A>C>E>D>BA > C > E > D > B, which means that Bob is the shortest.

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