264   This 2x3 grid has an interesting
200   property: 264x200 = 22x60x40.

Build a similar grid using all digits from 2 to 7.

Let's call the numbers ABC and DEF.

It is said that ABC x DEF = AD x BE x CF.

Since ABC x DEF is congruent do CxF (mod 10), and AD x BE x CF is congruent to D x E x F (mod 10), we have :

C x F congruent to D x E x F (mod 10).

C congruent to D x E (mod 10/F).

Since 10/F must be an integer, F could only be 2 or 5 (and indeed you have found F=2).

I"m working on this if I succeed in founding the solution, with no programming.

Posted by pcbouhid on 2005-03-29 20:07:14