## Ken's Puzzle of the WeekNine Digits in Sums

 A B C D E F G H I

Is it possible to find 3-digit numbers A,C,D,F, such that:

• A+D=G, and C+F=I
• B is the average of A and C.  E is the average of D and F.  H is the average of G and I.
• All digits 1-9 are used once in each row and column.

I'll admit I'm not sure if the complete puzzle can be solved.  If not, can it be solved if the 9-digits restriction applies only to the first two rows and the outside columns?

Source: Original.

Solutions were received from David Madfes, Keith F. Lynch, and Joseph DeVincentis.  All pointed out that it's not solvable as stated.  I'd be interested in any suggestions for making this a solvable puzzle.  Joseph provided a nice summary of all the <3> + <3> = <3> sums, included below.

173 + 286 = 459
173 + 295 = 468
127 + 359 = 486
127 + 368 = 495
162 + 387 = 549
218 + 349 = 567
128 + 439 = 567
182 + 394 = 576
216 + 378 = 594
152 + 487 = 639
251 + 397 = 648
218 + 439 = 657
281 + 394 = 675
182 + 493 = 675
215 + 478 = 693
143 + 586 = 729
142 + 596 = 738
124 + 659 = 783
214 + 569 = 783
134 + 658 = 792
243 + 576 = 819
352 + 467 = 819
142 + 695 = 837
241 + 596 = 837
317 + 529 = 846
125 + 739 = 864
271 + 593 = 864
214 + 659 = 873
324 + 567 = 891
234 + 657 = 891
243 + 675 = 918
342 + 576 = 918
341 + 586 = 927
152 + 784 = 936
162 + 783 = 945
317 + 628 = 945
271 + 683 = 954
216 + 738 = 954
215 + 748 = 963
314 + 658 = 972
235 + 746 = 981
324 + 657 = 981

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