Given whole numbers a and b we can find the ratio a/b and round it to the nearest whole percent.

A value of b is said to generate any percentage that is a possible value of a/b.

For example b=15 generates seven percentages between 0 and 50 including 27% = 4/15 and 47% = 7/15.
There is no smaller b that generates 47% but there is a smaller b (11) that generates 27% (3/11)

What is the smallest value of b such that for every percentage between 0 and 50 that it generates there is a smaller b that also generates it?

The smallest value of b is 20.

 5% =  1/20 ~= 1/19
10% =  2/20 ~= 1/10
15% =  3/20 ~= 2/13
20% =  4/20 ~= 3/15, 2/10
25% =  5/20 ~= 4/16, 3/12, 2/8, 1/4
30% =  6/20 ~= 3/10
35% =  7/20 ~= 6/17
40% =  8/20 ~= 6/15, 4/10, 2/5
45% =  9/20 ~= 5/11

Posted by Dej Mar on 2010-01-11 14:28:46