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 ABCD (Posted on 2006-11-26)
 A 2 0 3 0 2 2 B 1 3 0 3 0 2 C 1 2 2 1 3 0 A B C D 2 1 1 2 1 2 1 1 2 2 2 2 1 1 0 1 3 2 3 1 0 2 1 2 1 2 2 2 2 0
Every cell in the 6x6 grid contains one of four letters, namely, A, B, C or D. No letter can be horizontally or vertically adjacent to itself. The tables above and to the left of the grid indicate how many times each letter appears in that column or row.

Can you complete the grid?

 Submitted by Josie Faulkner Rating: 4.4118 (17 votes) Solution: (Hide) ``` +++++++++++++++++++++++++ A + 2 | 0 | 3 | 0 | 2 | 2 + +---+---+---+---+---+---+ B + 1 | 3 | 0 | 3 | 0 | 2 + +---+---+---+---+---+---+ C + 1 | 2 | 2 | 1 | 3 | 0 + +---+---+---+---+---+---+ A B C D + 2 | 1 | 1 | 2 | 1 | 2 + +++++++++++++++++++++++++++++++++++++++++ + 1 | 1 | 2 | 2 + A | B | C | D | C | D + +---+---+---+---+---+---+---+---+---+---+ + 2 | 2 | 1 | 1 + D | C | A | B | A | B + +---+---+---+---+---+---+---+---+---+---+ + 0 | 1 | 3 | 2 + C | B | C | D | C | D + +---+---+---+---+---+---+---+---+---+---+ + 3 | 1 | 0 | 2 + A | D | A | B | D | A + +---+---+---+---+---+---+---+---+---+---+ + 1 | 2 | 1 | 2 + D | B | D | C | A | B + +---+---+---+---+---+---+---+---+---+---+ + 2 | 2 | 2 | 0 + B | C | A | B | C | A + +++++++++++++++++++++++++++++++++++++++++``` Let r = row and c = column; let A, B, C and D refer to the entries in the grid. In r3, the three Cs must be in c1, c3 and c5, because C cannot appear in c6. This places B/D in c2, c4 and c6. In r4, two of the As must appear in c1 and c3, which places B/D in c2 and c4; A/D in c5 and A/B/D in c6. In c3, there must be an A in r6, which places A/C/D in r1; A/D in r2 and C/D in r5. In c5, there must be a C in r1, which places A/D in r2; A/C/D in r5 and A/C in r6. Now let us move to the rest of the options. In c1, r1 and r2 are A/B/D; r5 is B/D and r6 is A/B. As there are two Ds in the column, r5 must be a D. In c2, r1 and r2 are B/C/D; r5 and r6 are B/C. In c4, r1 is B/D; r2 and r5 are B/C/D and r6 is B/C. In c6, r1, r2 and r5 are A/B/D and r6 is A/B. As there must be two Cs in r6, c2 has to be one of them. This makes r5c2 a B; r4c2 a D; r3c2 a B; r1c2 a B and r2c2 a C. As the only B has now been placed in r3, the two remaining cells must be Ds. Now, we can place a B in r4c4. This makes r4c6 an A and r4c5 a D. From this, we can deduce that r2c5 is A, leaving r5c5 and r6c5 as A/C. Now, r2c6 has to be a B, leaving A/D in r1c6 and B/D in r5c6. In c4, there has to be a B in r6, which places a C in r6c5 and an A in r5c5. The only place for the other B in r5 is in c6, which makes r6c6 an A; r1c6 a D and r6c1 a B. Now, look at r1. The only place for the other C is in c3, which puts a D in r5c3; a C in r5c4 and an A in r2c3. As the only B has already been placed in r1, r1c4 must be D and r1c1 must be A. This puts a D in r2c1 and a B in r2c4.

 Subject Author Date re: the solution Josie Faulkner 2007-02-06 04:53:33 the solution axf 2007-02-05 05:04:22 re: nice and hard Josie Faulkner 2007-01-13 11:34:41 nice and hard assaf 2007-01-13 11:03:38 re: there might be other solutions also.... Josie Faulkner 2006-12-30 17:17:11 there might be other solutions also.... vivek 2006-12-30 16:46:04 re: No Subject Josie Faulkner 2006-12-29 06:04:35 No Subject Nevine 2006-12-14 10:02:41 No Subject Terry 2006-12-08 19:44:44 re: No Subject Josie Faulkner 2006-12-04 18:07:53 No Subject Chris 2006-12-04 14:33:07 re: Just wondering... Josie Faulkner 2006-11-29 03:07:59 Just wondering... George 2006-11-28 19:39:35 re(6): Another Solution? Josie Faulkner 2006-11-28 18:49:13 re(5): Another Solution? Penny 2006-11-28 18:09:50 re(4): Another Solution? Josie Faulkner 2006-11-28 13:57:18 re(3): Another Solution? Penny 2006-11-28 10:11:29 re: That was fun. Josie Faulkner 2006-11-28 02:45:15 re(2): Another Solution? Josie Faulkner 2006-11-28 02:42:19 That was fun. George 2006-11-27 21:28:58 re: Another Solution? Penny 2006-11-27 20:28:30 re: Great puzzle Josie Faulkner 2006-11-27 19:41:09 re: Another Solution? Josie Faulkner 2006-11-27 18:58:21 Another Solution? Guest 2006-11-27 18:18:38 Great puzzle tootone 2006-11-26 20:58:24 re: solution unique --- and how the computer program finds it Josie Faulkner 2006-11-26 14:49:46 re: If you got it, flaunt it! Josie Faulkner 2006-11-26 14:48:01 solution unique --- and how the computer program finds it Charlie 2006-11-26 13:07:29 If you got it, flaunt it! Federico Kereki 2006-11-26 12:52:13 re(2): Solution Josie Faulkner 2006-11-26 12:38:12 re: Solution Jyqm 2006-11-26 11:44:07 Solution Penny 2006-11-26 10:34:18

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