# Lack of unique solutions.

Bug #582271 reported by N. F. Taussig on 2010-05-18
This bug affects 1 person
Affects Status Importance Assigned to Milestone
Undecided
Unassigned

### Bug Description

The Multiplication Puzzle I did this morning did not have a unique solution. The desired solution was a correct solution, but the program did not recognize other valid solutions so it told me incorrectly that those solutions were not valid. It seems to me that the Multiplication Puzzle should be programmed to produce a unique solution or recognize all valid solutions.

In this particular problem, one of the factors was 11. Since the other factor had the form 1FC, this meant that the addends were 1FC and 1FC0. The only further restriction was that the product have the form 1HEC. There are many choices for C and F that result in a product of the form 1HEC in which the values of C, E, F, and H are distinct from each other, 0 (the value of the leading term), and 1. In this case, the program sought the answer 162 * 11 = 1782, but 124 * 11 = 1364, 132 * 11 = 1452, 142 * 11 = 1562 (among others) also work.

I suspect that the use of 11 as a factor and the fact that each sum was less than 10 contributed to the lack of a unique solution. However, this observation is based solely on the work I did on this interesting puzzle.

 N. F. Taussig (nftaus) wrote on 2010-05-18: #1