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A permutiple is a natural number that is a nontrivial multiple of apermutation of its digits in some base. Special cases of permutiples includecyclic numbers (multiples of cyclic permutations of their digits) andpalintiple numbers (multiples of their digit reversals). While cyclic numbershave a fairly straightforward description, palintiple numbers admit manyvarieties and cases. A previous paper attempts to get a better handle on thegeneral case by constructing new examples of permutiples with the same set ofdigits, multiplier, and length as a known example. However, the results are notsufficient for finding all possible examples except when the multiplier dividesthe base. Using an approach based on the methods of this previous paper, wedevelop a new method which enables us to find all examples under anyconditions.

A Method for Finding All Permutiples with a Fixed Set of Digits from a Single Known Example