Maths Olympiad Prep

Track / Stage 4 / 276 of 340 #536 of 1964

Problem 536

AMC 12 late, AIME early
Combinatorics Difficulty 5.0 Find the answer

Folklore

Three runners X-X, YY, and ZZ - are participating in a race. ZZ was delayed at the start and ran last, while YY ran second. During the race, ZZ changed places with other participants 6 times, and XX changed places 5 times. It is known that YY finished before XX. In what order did they finish?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Runner XX, who ran first, changed places with other runners an odd number of times, which means he finished second. Since YY finished before XX, he was first at the finish line, and ZZ was third.

## Answer

YY - first, XX - second, ZZ - third.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.