When the chairs in a hall are arranged in rows of 9, of 12 or of 16, 4 chairs are always left over. The hall has between 400 and 500 chairs. How many chairs are there?

Explanation

1. 01

   The count is 4 more than a multiple of $\operatorname{LCM}(9, 12, 16) = 144$.

2. 02

   Possible counts: 148, 292, 436, 580, …

3. 03

   The only one between 400 and 500 is 436.