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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.

See The Solution Submitted by K Sengupta    
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Solution program solution | Comment 3 of 4 |
 10   for Base=3 to 100
 20   for X=1 to Base-1:H=X*Base*Base
 30   for Y=1 to Base-1:T=Y*Base
 40   for Z=1 to Base-1:U=Z
 50     if H+T+U=X^X+Y^Y+Z^Z then print Base;X;Y;Z,H+T+U
 60   next
 70   next
 80   next
 90   next
 
base x1 x2 x3    decimal value lhs & rhs
4  1  3  1      29
4  3  1  3      55
25  5  1  3     3153
91  6  1  5     49782

 


  Posted by Charlie on 2009-04-13 02:55:02
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