(In reply to
re(3): Solution (as interpreted) by brianjn)
I had arrived at the same solution(s) as ed and Charlie. But, due to the large number of possible solutions, I tried to see if there could be an interpretation that might limit the bulk to a smaller, if not unique, set.
With the assumption that a solution might be sought such that each digit appeared only once in the set of bases, I arrived at the following:
 16_{14}, 36_{36}, 49_{20}, 64_{57}, 100_{98}
 16_{14}, 36_{36}, 49_{20}, 64_{58}, 100_{97}
 16_{16}, 36_{30}, 49_{24}, 64_{57}, 100_{98}
 16_{16}, 36_{30}, 49_{24}, 64_{58}, 100_{97}
 16_{16}, 36_{34}, 49_{20}, 64_{57}, 100_{98}
 16_{16}, 36_{34}, 49_{20}, 64_{58}, 100_{97}
The sum of the bases add to the perfect square 225 (15
^{2}).
Of these there are two sets with the minimum total of their base 10 values. This total is 76. (The other four sets total 80 each):
 16_{16}=10, 36_{30}=16, 49_{24}=21, 64_{57}=17, 100_{98}=12
 16_{16}=10, 36_{30}=16, 49_{24}=21, 64_{58}=16, 100_{97}=13

Posted by Dej Mar
on 20100707 08:16:52 