A pandigital alphametic

Question

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 — z100, Commented Apr 13 at 21:19

Aaron Windsor · Accepted Answer · 2024-04-14 00:50:18Z

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.

answered Apr 14 at 0:50

Aaron Windsor

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