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50 - Digit Number II (Posted on 2010-05-29) Difficulty: 2 of 5
N is a duodecimal (base 12) positive integer having precisely 50 digits such that each of its digits is equal to 1 except the 26th digit. If N is divisible by the duodecimal number 17, then find the digit in the 26th place.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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re: analytical solution | Comment 5 of 9 |
(In reply to analytical solution by Daniel)

"well if x is the missing digit then the base 10 representation of N is

N = x*12^25 + sum(12^t, t=0 to 24) + sum(12^t, t=26 to 49)"
 
Why 12^25?
 
Sorry, I see: you're counting the 26th digit starting on the right as the first. My solution assumes counting from the left, so it's the 25th from the right, with value 12^24.

  Posted by Charlie on 2010-05-29 16:02:11
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