Competition problem — Combinatorics

Library / /13 of 32

Combinatorics Difficulty 5.1 AIME, harder Find the answer Netherlands

Three wheels are pushed together so they don't slip if we turn them. The circumferences of the wheels are $14$ , $10$ , and $6$ cm, respectively. On each wheel an arrow is drawn, pointing downwards. Someone turns the big wheel and the other wheels turn with it. This stops at the first moment all arrows point downwards again. Every time one of the arrows is pointing up, a whistle sounds. If two or three arrows point up at the same time, only one whistle sounds. How many whistles sound in total?

Your answer

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

Solution

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.