It turns out that the common logarithms of each of the numbers from 2 through 9 can be very well approximated by rational numbers of the form n/40.
Derive each of the numerators with no calculation aids beyond pencil and paper.
(In reply to
A start (spoiler) by Steve Herman)
log 5 = log 10  log 2 ~= 1  12/40 = 28/40
and perhaps for 7 we just need to interpolate between 31/40 for 6 and 36/40 for 8, with 34/40 giving the extra half point to the lower side (a 32 split instead of 23) as the intervals between logs get lower as the numbers get higher.
Edited on May 31, 2011, 2:50 pm

Posted by Charlie
on 20110531 14:43:51 