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No repeated numbers (Posted on 2008-08-20) Difficulty: 2 of 5
Look at the 8x8 grid below at left. In the rows and columns there are repeated numbers. Erasing 19 of them, we achieve the grid at right, that has no repeated numbers in any row, in any column.
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 5 | 7 | 1 | 2 | 5 | 4 | 4 | 3 |       |   | 7 | 1 |   | 5 |   | 4 | 3 |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 4 | 3 | 1 | 2 | 7 | 5 | 6 | 3 |       | 4 | 3 |   | 2 | 7 | 5 | 6 |   |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 5 | 5 | 3 | 4 | 2 | 1 | 7 | 8 |       |   | 5 | 3 |   | 2 |   | 7 | 8 |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 6 | 6 | 2 | 7 | 3 | 3 | 3 | 1 |       | 6 |   | 2 | 7 |   | 3 |   | 1 |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 3 | 2 | 5 | 6 | 9 | 1 | 8 | 6 |       | 3 | 2 | 5 |   | 9 | 1 | 8 | 6 |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 2 | 1 | 3 | 4 | 6 | 2 | 5 | 2 |       |   | 1 |   | 4 | 6 |   | 5 | 2 |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 9 | 8 | 4 | 1 | 4 | 6 | 2 | 3 |       | 9 | 8 | 4 | 1 |   | 6 | 2 |   |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
| 7 | 5 | 6 | 5 | 8 | 5 | 1 | 4 |       | 7 |   | 6 | 5 | 8 |   | 1 | 4 |
+---+---+---+---+---+---+---+---+       +---+---+---+---+---+---+---+---+
Do the same with this 8x8 grid, erasing the minimum number of squares.
                    +---+---+---+---+---+---+---+---+
                    | 8 | 4 | 6 | 5 | 3 | 5 | 7 | 4 |
                    +---+---+---+---+---+---+---+---+
                    | 6 | 5 | 5 | 4 | 7 | 8 | 3 | 1 |
                    +---+---+---+---+---+---+---+---+ 
                    | 5 | 7 | 2 | 5 | 5 | 4 | 8 | 7 |
                    +---+---+---+---+---+---+---+---+
                    | 8 | 6 | 5 | 3 | 2 | 5 | 4 | 4 |
                    +---+---+---+---+---+---+---+---+
                    | 3 | 8 | 1 | 4 | 8 | 6 | 5 | 2 |
                    +---+---+---+---+---+---+---+---+ 
                    | 5 | 3 | 7 | 6 | 4 | 2 | 2 | 2 |
                    +---+---+---+---+---+---+---+---+
                    | 5 | 8 | 7 | 7 | 6 | 2 | 1 | 3 |
                    +---+---+---+---+---+---+---+---+
                    | 1 | 1 | 3 | 7 | 6 | 4 | 6 | 8 |
                    +---+---+---+---+---+---+---+---+ 

See The Solution Submitted by pcbouhid    
Rating: 4.0000 (3 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answer this postPittmanBetty2011-10-22 09:01:08
reply this postArleneFOX192011-10-22 06:38:29
Solution2880 solutions; 6 HitoriCharlie2008-08-24 13:10:41
re(5): ===== so, you beat them?Steve Herman2008-08-24 08:25:46
SolutionComputer solution at lastCharlie2008-08-23 17:11:48
re: A look at minimalityCharlie2008-08-22 10:51:57
A look at minimalityGamer2008-08-21 17:04:55
re(4): ===== so, you beat them? (Spoiler)pcbouhid2008-08-21 12:36:46
re(3): ===== so, you beat them? (Spoiler)Dej Mar2008-08-21 09:56:29
re(2): ===== so, you beat them?pcbouhid2008-08-21 08:39:31
re:brianjn2008-08-21 00:28:09
optimal algarithm (no proof)Daniel2008-08-21 00:12:55
re: "HITORI"Dej Mar2008-08-21 00:10:25
SolutionCross Referencingbrianjn2008-08-20 23:40:54
"HITORI"pcbouhid2008-08-20 22:09:27
Now, can we prove this is minimal?ed bottemiller2008-08-20 17:13:26
SolutionA solutionDej Mar2008-08-20 17:00:30
Those Fives!ed bottemiller2008-08-20 16:47:05
As a Start...ed bottemiller2008-08-20 16:20:19
possible solution (spoiler)Daniel2008-08-20 15:35:42
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