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Duodecimal Element Sum Settlement (Posted on 2016-05-25) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Solution working in decimal, same answer | Comment 2 of 3 |
(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.

  Posted by Charlie on 2016-05-25 14:22:58
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