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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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re: A similar problem but perhaps a bit trickier | Comment 16 of 39 |
(In reply to A similar problem but perhaps a bit trickier by Kirk)

Since 10 is -1 mod 11, we can calculate the alternating sum of the digits and easily find that x=7. A similar method, employing the values of 10^n mod 13, can be used on the original problem, but it would be laborious due to the large number of digits.
  Posted by Richard on 2003-11-20 17:47:15

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