If we assume that 11 meters = 12 yards, what is the smallest integral number of meters that can be converted to its equivalent integral number of yards simply by rearranging the order of the digits of the number?

What if we do the same with the actual exact equivalents?: 1143 meters = 1250 yards.

Then try your hand at 228 solar months = 235 lunar months (the 19-year Metonic cycle).

Note that rearranging the digit order changes a number by a multiple of 9.  You can use this fact to show that the numbers of meters and yards must both be multiples of 9.

This at least quickens the hunt.

Posted by Jer on 2007-10-04 15:26:36