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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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Solution Standard solution | Comment 6 of 17 |
There's a standard way of solving this kind of "move-to-the-beginning" problems. Assume the solution is a number abc...3 and let X be the continued fraction

Then, (X+3)/10= 0.3abc...3abc...3abc..., which must be equal to 3X.

Equating, we get X=3/29, which works out to be 0.1034482758620689655172413793..., so our number is 1034482758620689655172413793.
Edited on March 1, 2004, 12:01 pm
  Posted by Federico Kereki on 2004-03-01 12:00:48

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