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50 - Digit Number II (Posted on 2005-05-13) Difficulty: 2 of 5
I am thinking of a fifty-digit number divisible by 239, of which, each digit is the same, except the ones digit. What is the ones digit?

See The Solution Submitted by Dustin    
Rating: 2.8000 (5 votes)

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Some Thoughts Assuming leading zeroes Comment 11 of 11 |
(In reply to Puzzle Solution by K Sengupta)

If we assume leading zeroes, so that we have 49 zeroes followed by the ones digit(t), then with the usual definition of B as in the last post, the value of B is simply t, which cannot be divisible by 239, unless t=0, since gcd(t, 239) = 1

However, in this situation, we have the same digit, that is 0, repeated 50 times. This is a contradiction.

Consequently, the given number cannot admit of leading zeroes. 

  Posted by K Sengupta on 2008-05-18 02:25:02
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