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Powering up the digits II (Posted on 2009-10-22) Difficulty: 3 of 5
Each of X1, X2 and X3 represents a nonzero digit of the 3-digit base M positive integer X1X2X3; where X1, X2 and X3 are not necessarily distinct.

Determine the respective minimum and maximum positive integer value of M, with M < 100, such that this equation has at least one valid solution.

X1X1 + X2X2 + X3X3 = X1X2X3 - 1

Note: X1X2X3 denotes the concatenation of the three digits.

  Submitted by K Sengupta    
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Solution: (Hide)
There exists only one solution to the given equation, which is as follows:
4             3  2  3         59
base      representation   decimal value
As a check:
3^3 + 2^2 + 3^3 = 59 - 1 (decimal representation)

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

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutioncomputer solutionCharlie2009-10-22 18:00:31
SolutionNo SubjectAdy TZIDON2009-10-22 15:39:24
No SubjectAdy TZIDON2009-10-22 15:37:45
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