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