How many three-digit numbers have an odd number of factors? 
Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
It can be shown that a positive integer has an odd number of factors if and only if it is square. ~The smallest three-digit square number is $${{10}^{2}}=100$$ and the largest is $${{31}^{2}}=961$$. Hence there are $$31-9=22$$ three-digit numbers which have an odd number of factors. 