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.
29*6=58*3=174
39*4=78*2=156
Method:
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.
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Posted by Jer
on 2016-06-07 11:33:35 |
Exhausted Spoiler
