What is the least possible numbers in a Math Circle, where girls constitute more than 48.5% but less than 50% of the members?
We have had a few problems dealing with finding a fraction between a pair of specified values, where the fraction is to have the smallest possible denominator.
A standard method to solve these is to use continued fractions. Pretty easy when Wolfram can do the number crunching for you.
0.485 = [0; 2, 16, 6]
0.5 = [0; 2]
The smallest continued fraction between these is [0; 2, 17] = 17/35.
This was a pretty easy problem as far as continued fractions go, easy enough that Steve's assumption of n/(2n+1) gets to the same answer. For comparison look at
Minimizing the Denominator for a problem with the same idea but much harder to tackle without continued fractions.
Solution via Continued Fractions
