Contribution for Puzzlet #078
From:  Ken Duisenberg [ken.duisenberg@hp.com]

No computer needed, as a little analysis will yield the result. Each answer is a multiple of 111, which has as factors 37 and 3. So one of each pair of numbers must be either 37 or 74, and the other must have a factor of 3.

This leads quickly to the table:

37 x 12 = 444
37 x 15 = 555
37 x 18 = 666
37 x 21 = 777
37 x 24 = 888
74 x 12 = 888

37x27=999 is not an answer due to digit duplication, and any other multiples would yield more than 3 digits.

If leading zeros are allowed, then the additional answers below would be added:

37 x 06 = 222
37 x 09 = 333


Thanks for the e-mail. Duhh! Why didn't I think of that? Very simple - and elegant. I'm going to put it on my contributions page. However, I'll leave the computer solution in, as I know a lot of readers of my page enjoy finding the answers that way. The coding is always fun.

Dave.


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