Juha Saukkola
476
238
510
Hi ed
Answer to the 3x3 GCD17 puzzle posted 20-June is as follows
425
731
680
Regards
Pete Kogel
ed:
i've tinkered around with some algorithms and have come up with a couple of
answers for the challenge, here they are:
[ [ 4 2 5 ] , [ 7 3 1 ] , [ 6 8 0 ] ]
[ [ 9 1 8 ] , [ 3 0 6 ] , [ 5 2 7 ] ]
perhaps a bit "cheating" to write a program to find them, but it was
interesting nonetheless. They all seem to check. All six rows/columns are
divisible by 17.
-Regards,
David Perryman
> The greatest common divisor for 3x3 squares using 0-9 without
> repetition is 17.
935
102
867
--
Roger Phillips, senior software engineer
I believe your Number Squares Puzzle has two different solutions:
425
731
680
and
918
306
527
Peter Exterkate
Ed --
I don't know if this is unique, I found it by hacking and slashing as usual.
425
731
680
Was the puzzle correctly specified? 0-9 without repetition is 10 digits,
which don't fit. I didn't use the 9.
Method: List all 53 3-digit multiples of 17. Eliminate the 14 that contain
repeating digits. Notice the most constraining digits (there are only 3
multiples beginning with 2, for example) and use those to abbreviate
testing of combinations. Fill the left column and top row first during each
test, not using any multiples that contain zeroes. 1, 2, 3 ruled out as
upper left digits by trying each combo and finding spots that can't be
filled from the menu of legal multiples. 4 works, as above. There may be
more, but laziness sets in.
Take care --
David Yamanishi
{425, 731, 680}
George Tolley
918
306
527
Whew!
--mathidentity
An exhaustive search doesn't take long:
425
731
680
j k mclean
Hi Ed,
Yes!!!
935
102
867
Alastair Cuthbertson
918
306
527
Thanks, Jeff Gosselin.
Using 0-9 was a bit difficult - trying to put 10 digits in 9 slots
0-8 will yield
204
357
816
Bill Downs
Mableton, GA 30126