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Powering up the digits (Posted on 2009-04-12) Difficulty: 2 of 5
Each of x1, x2 and x3 corresponds to a nonzero digit, whether same or different, in positive integer base b.

Determine all possible value(s) of b ≤ 100 such that this equation has at least one valid solution:

x1x2x3 = x1x1 + x2x2 + x3x3

Note: x1x2x3 corresponds to concatenation of the three digits.

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
b = 4, 25 and 91 are the only possible values ≤ 100.

There are precisely two solutions in base 4,and:

There is precisely one solution in base 25, and:

There is precisely one solution in base 91.

For an explanation, refer to the solution submitted by Charlie in this location.

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Daniel has extended the provisions corresponding to the given problem in his location, exploring the cases where each of x1, x2 and x3 is between 1 and 99, and has found a solution each for base 904 and base 215.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
more solutionsDaniel2009-04-13 14:54:01
Solutionprogram solutionCharlie2009-04-13 02:55:02
SolutionsolutionDej Mar2009-04-12 21:41:33
computer solution (spoiler)Daniel2009-04-12 17:06:14
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