Place one of A, B, C or D into each of the 25 empty squares so that the number of letters in each row and column match the number indicated on that row and column for that letter.
Identical letters cannot be next to each other vertically or horizontally, but may be adjacent diagonally.
+---+---+---+---+---+
A | 2 | 0 | 2 | 2 | 2 |
+---+---+---+---+---+
B | 1 | 2 | 0 | 2 | 0 |
+---+---+---+---+---+
C | 1 | 2 | 1 | 0 | 1 |
+---+---+---+---+---+
A B C D | 1 | 1 | 2 | 1 | 2 |
+---+---+---+---++===+===+===+===+===+
| 2 | 1 | 1 | 1 || | | | | |
+---+---+---+---++---+---+---+---+---+
| 2 | 1 | 0 | 2 || | | | | |
+---+---+---+---++---+---+---+---+---+
| 2 | 2 | 1 | 0 || | | | | |
+---+---+---+---++---+---+---+---+---+
| 0 | 1 | 2 | 2 || | | | | |
+---+---+---+---++---+---+---+---+---+
| 2 | 0 | 1 | 2 || | | | | |
+---+---+---+---++---+---+---+---+---+
From Mensa Puzzle Calendar 2020 by Fraser Simpson, Workman Publishing, New York. Puzzle for December 30.
CDABA
ABDAD
BCABA
DBCDC
ACDAD
I found it easiest to fill in all of a single letter at a time. Here's a quick explanation of how I did it, numbering rows and columns 1-5 from top to bottom and left to right, respectively:
Row 3 contains two Bs. They can't be adjacent, and there are no Bs in columns 3 or 5, so [3,4] must be B. We need another B in column 4 and the only valid cell is [1,4]. We need two Bs in column 2 and the only valid cells are [2,2] and [4,2]. We need another B in row 3 and the only valid cell is [3,1]. Finishing row 3 we put a C in [3,2] and As in [3,3] and [3,5].
Row 2 contains two As. They must be in [2,1] and [2,4]. Following similar logic we then know [5,4], [5,1], [1,3] and [1,5] must be the remaining As in the grid.
Moving on, [2,3] and [2,5] must be D. Then [4,4], [4,1], [1,2], [5,3] and [5,5] must be D.
The remaining empty squares are filled in with C to complete the solution.
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Posted by tomarken
on 2021-01-07 08:19:25 |
Solution
