Find, as Ed Pegg did, at least one solution of this pandigital alphametic:

                     A x BC x DEF = GHIJ.

How many solutions does it have altogether?

(GHIJ is thus a Melissa number, one which can be expressed as the product of numbers none of which uses any of the digits in the original number.)

  • $\begingroup$ Not so important, but Is B,D or G equal zero alowed? $\endgroup$
    – z100
    Commented Apr 13 at 21:19

1 Answer 1


If we don't allow B, D, or G to equal zero, there are:

Only two solutions:

1 x 26 x 345 = 8970

2 x 14 x 307 = 8596

If we allow B, D, or G to equal zero, there are:

70 more solutions with either B or D equal to zero. There are no solutions with G equal to zero.

I verified these answers with a SAT solver.


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