If we only consider problems with decimal numbers as above there is no possibility of any hardness result, because there are only 10! different assignments of digits and letters to try. Therefore we will generalize the problem slightly: the base of representation for our numbers will be given as part of the problem (expressed in unary or binary) rather than always being decimal, and we will allow the puzzle to contain arbitrarily many different letters (up to the base of representation). The… CONTINUE READING