Maths Olympiad Prep

Track / Stage 4 / 200 of 340 #460 of 1964

Problem 460

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

## 29. Eiffel Tower and Flower Hat

If every American woman from Minnesota wears a flower hat while visiting the Eiffel Tower, and if every visitor to the Eiffel Tower who wears a flower hat is an American woman from Minnesota, can we conclude that all American women from Minnesota who wear a flower hat visit the Eiffel Tower?

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

29. Of course not: it is quite possible that a certain American woman from Minnesota wears a hat with flowers but does not visit the Eiffel Tower.

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