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50 - Digit Number (Posted on 2003-11-15) Difficulty: 3 of 5
A number of 50 digits has all its digits equal to 1 except the 26th digit. If the number is divisible by 13, then find the digit in the 26th place.

See The Solution Submitted by Ravi Raja    
Rating: 3.3333 (6 votes)

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Solution a little more straightforward | Comment 4 of 39 |
note that 111111 is divisible by 13. (13*8547)

likewise every group of six consecutive ones in the 50 digit number is divisible by sixteen.

Removing the first and last 24 (4*6) digits of our 50 digit number leaves us with only the 25th and 26th digit.

the 25th digit is 1 and therefore the 26th must be 3 since 13 is divisible by itself.

That said, I very much appreciate the elegance of Charlie's solutions.
  Posted by Eric on 2003-11-16 01:07:26
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