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Doubles on reverse (Posted on 2008-09-02) Difficulty: 2 of 5
In the problem "Mirror, mirror on the wall" it was proved that no number in the decimal system doubles on reversing its digits, and answered for bases 3, 5 and 8 (base 2 has leading zero, so itīs not valid).

Generalise the answer for positive integer bases.

  Submitted by pcbouhid    
Rating: 3.0000 (1 votes)
Solution: (Hide)
Itīs a reazonable long analytical proof. The answer is: this can only happens in numbers systems whose bases are either multiples of 3 or 2 more than a multiple of 3.

Note that 10 is not a multiple of 3 neither 2 more than a multiple of 3.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsSome patterns given (spoiler)Dej Mar2008-09-03 01:00:41
SolutionAnalytic solutionPaul2008-09-02 23:12:54
Some Thoughtscomputer exploration -- some answers givenCharlie2008-09-02 17:43:46
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