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Move the 2 - double the number (Posted on 2002-04-19) Difficulty: 3 of 5
A certain number ends with the digit 2. Moving the 2 from the end of the number to its front doubles it. Can you find this number?

(Hint: it's quite large)

See The Solution Submitted by levik    
Rating: 4.1111 (9 votes)

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Solution Infinitely many | Comment 7 of 10 |

I think the easiest way to get the solution is to realize that if 2 is in the ones place before doubling, then a 4 must be in the ones place after doubling. Then it becomes simple addition.

    .... X 4 2

    ... X 4 2 +

   .... Y X 4

The first solution is when X finally becomes a 1 without a carryover. The number is 105263157894736842. Unless I made a sloppy addition error. This solution is not unique and there is in fact infinitely many of them.

The second solution is continuing the process again until the number 1 is reached once more without a carryover. This number is 105263157894736842105263157894736842, (unless I have made an addition error in the first part). This number has all the same properties of the first. The process can, without a doubt, go on as long as you have room to write all of the digits down.

  Posted by Michael Cottle on 2004-12-31 23:13:01
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