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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)

  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

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionThe numberMath Man2015-11-08 19:30:18
re: The continued fraction wayTheKPAXian2009-10-06 19:48:57
answerK Sengupta2007-06-28 23:03:30
SolutionInfinitely manyMichael Cottle2004-12-31 23:13:01
SolutionThe continued fraction wayFederico Kereki2003-12-04 09:49:37
SolutionAnother methodDJ2003-06-25 16:07:43
another methodCharlie2003-06-04 04:01:16
another approachsteve2003-05-22 03:09:30
My AnswerTom2002-05-09 12:15:01
Typo in your solutionFingLao2002-05-09 09:43:32
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