S denotes the set of rational numbers that are expressible as repeating duodecimal fractions of the form:
0.TUVWXTUVWX......., where T, U, V, W and X are distinct base 12 digits.
Determine the sum of the elements of S.
Note: Every number below is written in base 12.
There are 10xBxAx9x8 = 47000 possible 5duodigit strings. Each of 0 through B appears 4700 times in each position. The numbers 0 through B sum to 56. 4700x56=212600.
This is the sum of duodigits in each position.
The duodigits in the 1/10 place sum to 21260
The duodigits in the 1/100 place sum to 2126
The duodigits in the 1/1000 place sum to 212.6
etc.
These numbers sum to 235BB.BBBBBBBB...
or 23600
(The number in base 10 is 47520.)

Posted by Jer
on 20160525 13:14:55 