Clement Wood, in his rare "Book of Mathematical Oddities" asserts that AB*C=DE*F=GHI
(distinct letters represent distinct digits) has only 2 solutions.
It is left to you to validate (or to disprove) his statement.
Write down all possible B,C,I
there need to be at least two pairs B,C that lead to the same I. This leaves
I=2: B,C = 3,4 or 6,7 or 4,8 or 8,9
I=4: B,C = 2,7 or 3,8 or 6,9
I=6: B,C = 2,3 or 2,8 or 4,9 or 7,8
I=8: B,C = 2,4 or 3,6 or 4,7 or 2,9
I couldn't see how to narrow the possibilities so I went the exhaustive route from here.
For each of the I cases, make a list of each possible AB*C and AC*B with the product, provided this doesn't repeat a digit.
Search the list for two products with the same GHI.
Make sure we actually get distinct digits of AB*C and DE*F.
The only two solutions that arose are those above.
Posted by Jer
on 2016-06-07 11:33:35