Neighboring Multiples (Posted on 2009-03-15)

  9 5 1
  6 7 2
  4 3 8
 

	Submitted by Charlie
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All the rotations and reflections of the one solution are shown below: 2 6 5 7 3 1 9 8 4 2 7 9 6 3 8 5 1 4 4 1 5 8 3 6 9 7 2 4 8 9 1 3 7 5 6 2 5 1 4 6 3 8 2 7 9 5 6 2 1 3 7 4 8 9 9 7 2 8 3 6 4 1 5 9 8 4 7 3 1 2 6 5 CLS e = 3: GOSUB try e = 5: GOSUB try e = 9: GOSUB try END try: taken(e) = 1 FOR a = 1 TO 9 IF taken(a) = 0 THEN taken(a) = 1 FOR b = 1 TO 9 IF taken(b) = 0 THEN taken(b) = 1 FOR c = 1 TO 9 IF taken(c) = 0 THEN taken(c) = 1 FOR d = 1 TO 9 IF taken(d) = 0 AND (b + d + e) MOD a = 0 THEN taken(d) = 1 FOR f = 1 TO 9 IF taken(f) = 0 AND (b + e + f) MOD c = 0 _ AND (a + c + d + e + f) MOD b = 0 THEN taken(f) = 1 FOR g = 1 TO 9 IF taken(g) = 0 THEN taken(g) = 1 FOR h = 1 TO 9 IF taken(h) = 0 AND (d + e + h) MOD g = 0 THEN taken(h) = 1 FOR i = 1 TO 9 IF taken(i) = 0 AND (h + e + f) MOD i = 0 _ AND (b + c + e + h + i) MOD f = 0 _ AND (g + d + e + f + i) MOD h = 0 _ AND (a + b + e + g + h) MOD d = 0 THEN taken(i) = 1 PRINT a; b; c: PRINT d; e; f: PRINT g; h; i: PRINT taken(i) = 0 END IF NEXT taken(h) = 0 END IF NEXT taken(g) = 0 END IF NEXT taken(f) = 0 END IF NEXT taken(d) = 0 END IF NEXT taken(c) = 0 END IF NEXT taken(b) = 0 END IF NEXT taken(a) = 0 END IF NEXT taken(e) = 0 RETURN From Giant Book of Mensa Mind Challenges, edited by Todd Johnson, Section 3: "Nearly Impossible Brain Bafflers", page 197.

	Subject	Author	Date
	Puzzle Answer	K Sengupta	2023-08-20 22:28:48
	Computer solution	Robby Goetschalckx	2009-03-15 14:08:44