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 Move the 2 - double the number (Posted on 2002-04-19)
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)

 Submitted by levik Rating: 4.1111 (9 votes) Solution: (Hide) The number is 105263157894736842. Hey, I said it was quite large, didn't I? Start by realizing that the second to last digit of the original number is 4. (This is because the new number's last digit has to be double the old last digit which was two. And the new last digit is the original next to last digit - everything gets shifted when you move the 2 to the front). Next write down:``` ..42 + ..42 = ...4``` (This is because you are doubling the first number to get the new one.) It will become obvious that the second to last digit of the new number (and third to last of the new one) is 8: ``` ...842 + ...842 = ....84``` Note that for the next step, 8+8 will be 16, and so we will use the 6 as the third to last digit for the new number, but remember to carry over the 10 for the next time, when 6+6+1 will yield 13: ``` ...6842 + ...6842 = ...3684``` If you keep this up long enough (don't get discouraged, but be careful in your arithmetics) you will eventually get a valid equasion: ``` 105263157894736842 + 105263157894736842 = 210526315789473684```

 Subject Author Date The number Math Man 2015-11-08 19:30:18 re: The continued fraction way TheKPAXian 2009-10-06 19:48:57 answer K Sengupta 2007-06-28 23:03:30 Infinitely many Michael Cottle 2004-12-31 23:13:01 The continued fraction way Federico Kereki 2003-12-04 09:49:37 Another method DJ 2003-06-25 16:07:43 another method Charlie 2003-06-04 04:01:16 another approach steve 2003-05-22 03:09:30 My Answer Tom 2002-05-09 12:15:01 Typo in your solution FingLao 2002-05-09 09:43:32

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