One day tom was playing with numbers.he wrote 11 fractions using all natural numbers from 1 to 22 exactly once, either as numerator or as denominator.how many of these fractions,at most,are integers?
The only way to get 10 is if one of 13,17, or 19 is paired with 1. WLOG suppose 13 is paired with 1.
13/1
17/19
We have 18 numbers left and want to find the max. number of integers we can obtain. Here is a possible solution.
22/11
21/7
20/10
18/9
16/8
15/5
14/2
12/4
6/3
It is indeed 10.