If x<1, then (1-x)(1+x)<1
We will want to keep number as small as possible, but when choose a number less than 1 we have to choose another number much greater than 1 to compensate, ex. for 0.5 we have to choose >2, 0.1 we have choose >10. So for optimal solution we end up choosing 1.
But all can not be 1, so we end up choosing 18 1s and 1 2.
It needs more rigorous proof though.