# Fuzzy'ss....

**Number Theory**Level 3

A three digit number,written in the form \(abc\) ,is called fuzzy if \(abc\) is divisible by 7,the two digit number \(bc\) is divisible by 6,the digit \(c\) is divisible by 5,and the three digits a,b and c are all different.How many fuzzy numbers are there?

This problem was taken from Australian Mathematics Competition 2014