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Transfer of initial digit (Posted on 2012-12-20) Difficulty: 2 of 5
Prove that there does not exist a natural number, which upon transfer of its initial digit to the end, is increased five, six or eight times.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution I believe that there is a limit | Comment 1 of 2
The smallest digit one would be able to transfer is 1.
The largest number able to be formed would begin with 9.

Let the smallest number be:
On transfer the number becomes:
The smaller number will approach 1/5 of the larger but never equal it.  Since this is the limit any number greater than 5 can be disregarded.

  Posted by brianjn on 2012-12-20 18:04:58
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