Olympiad Maths Prep

Track / Stage 5 / 222 of 400 #822 of 2000

Problem 822

AIME late
Combinatorics Difficulty 5.5 Prove it

6. In the village of Monkeyville, every boy knows all the girls who know him, and among the acquaintances of each girl, the number of boys is greater than the number of girls. Prove that in Monkeyville, there are no fewer boys than girls.

## 7th grade

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

90.6. See the solution of problem 90.19, considering boys as knights and girls as liars.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.