Maths Olympiad Prep

Track / Stage 4 / 264 of 340 #524 of 1964

Problem 524

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. Spacing and $ signs are ignored.

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 and solution reproduced as published; topic, difficulty and ordering added by this site.