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.
(In reply to
Solution (assuming I kept my bases straight) by Jer)
There will be 12!/7! = 95040 such numbers, each being its own version of the value of TUVWX divided by (12^5 - 1) decimal. Each duodecimal digit will appear an equal number of times in each position, so that number will be 11!/7! = 7920 times.
The sum of the integers from 0 to 11 is 66, so the sum of the unreduced numerators will be
66*(12^4 + 12^3 + 12^2 + 12 + 1)*7920 = 11824449120
As mentioned, the denominator is 12^5 - 1 = 248831.
The unreduced answer is 11824449120/248831. Reduced, that is 47520 decimal.
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Posted by Charlie
on 2016-05-25 14:22:58 |
working in decimal, same answer
