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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 Solution (assuming I kept my bases straight) | Comment 1 of 3
Note: Every number below is written in base 12.

There are 10xBxAx9x8 = 47000 possible 5-duodigit 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 2016-05-25 13:14:55
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