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Move the 3, Triple the number (Posted on 2004-03-01) Difficulty: 2 of 5
If you moved the 3 at the end of a certain large number to the beginning, it would be the same as multiplying it by 3. What is the number?

See The Solution Submitted by Gamer    
Rating: 3.2000 (5 votes)

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re: complete set of answers, mathy reasoning *** correction | Comment 13 of 17 |
(In reply to complete set of answers, mathy reasoning by empraptor)

The general formula should read

X = (10^(28*n) - 1) * 3 / 29     where n is an integer >= 1

I made a mistake in doing modular math.  10^(29*n+28) is NOT congruent to 1 mod 29 for all n.  For example, 10^(29+28) = 1-^57 is congruent to 10 mod 29.

Because 10^28 is congruent to 1 mod 29,  10^28 * 10^28 should also be congruent to 1 mod 29.  If you extend this reasoning, 10^(28*n) is congruent to 1 mod 29 for all integer n >= 0.

Of course, while n=0 does satisfy the equation we set up to model the problem statement, it is not a valid solution because X=0 in that case.  So we limit n to >= 1.

  Posted by empraptor on 2004-03-04 03:44:36
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