ABCD Puzzles: Torture or Teacher?

Disclaimer

2014-0602 Puzzle HeadI did not receive approval to use the puzzle I wanted to use in this post, so I created an ABCD puzzle from scratch. Creating a puzzle was an excellent learning opportunity, so I am actually thankful I did not receive approval to use the puzzle I wanted to use. However, I would not be disappointed if, at some point in the future, I received approval. I chose to write this post because designing, attempting to solve, and solving an ABCD puzzle was a fantastic brain exercise.

Instructions

Every cell in the 6 x 6 grid contains one of four letters: A, B, C, or D. No letter can be horizontally or vertically adjacent to itself – for example, two adjacent cells cannot both contain the letter “C.” The tables above and to the left of the grid indicate how many times the letter appears in that column or row. The goal is to fill each of the 36 cells with the correct letter, such that all cells contain a letter that does not violate the puzzle rules or hints (if any are provided). The following puzzle contains five Givens (completed cells). Can you complete the grid?

Puzzle

2014-0610 ABCD Puzzle

Tips and Strategies

Do not read anything in this section unless you are absolutely certain you need help solving the puzzle. The following tips and strategies are not the only ones, or necessarily the best ones, applicable to ABCD puzzles. The following tips and strategies are specific to the puzzle featured in this post, but similar tips and strategies may help you solve similar puzzles.

I added the red letters and numbers below and to the right of the grid to improve communication and understanding. The hint “A” I added to the grid appears at the intersection of column R and row 2 (R2). Similarly, the “B” I added appears at the intersection of column M and row 5 (M5).

Tips

Tip 1: Use a pencil, rather than a pen, and keep an eraser nearby.

Tip 2: Look for a row or column that contains three of the same letter, and the row or column touches (vertically or horizontally) a cell in which the content is known. Any row or column that contains three of the same letter MUST include that letter in one of the first two cells, in one of the middle two cells, and in one of the last two cells of that row or column if you have a 6 x 6 grid.

Tip 3: Use a variety of strategies to solve ABCD puzzles. You cannot solve the featured puzzle with only the previous tips and following strategies. However, the ABCD puzzle would not be a cognitive challenge if I provided all the tips, strategies, or answers. Good luck.

Strategies

The puzzle tells us that column M contains 2 A’s, 3 B’s, 1 C, and 0 D’s. Since the puzzle also tells us we already have one B in the column, we also know the remaining B’s must be located at M3 and M1 because the rules tell us no letter can be adjacent to itself.

Cells M5 and N6 are given (B and D respectively), and we know from the puzzle M6 must be an “A” or “C.” However, the puzzle also tells us cell M6 cannot contain an “A” so it must contain a “C.” We now know the location of the one “C” and all three “B’s” in column M. According to the puzzle, the two empty cells in column M must both contain an “A.”

We can solve row 6 using the same strategy. M6, N6, and R6 are known. All we have to solve in row 6 are O6, P6, and Q6. The puzzle tells us Q6 cannot contain an “A” or “C.” Since the one “D” in row 6 was given, Q6 must contain a “B.” According to the puzzle, P6 cannot contain an “A” or “B.” Since we already know where the one “D” is located in row 6, we know P6 must contain a “C.” O6 is the only unsolved cell in row 6, and we still need one “B” in row 6, therefore O6 must contain the “B.”

Variations

You can find an example of some of the following variations here:

  • Eliminate hints from the grid.
  • Change the number of letters used – ABC, ABCD, ABCDE, etc.
  • Supersize the grid – an ABCD puzzle could be almost any size imaginable.
  • Substitute letters for numbers in clues above and to the left of a grid (Crypto)
  • Substitute symbols for numbers in clues above and to the left of a grid (Crypto)
  • Change the grid shape (Hexgrid)
  • Add a Rule – no letter can be diagonally adjacent to itself
  • Eliminate cells from the grid – blackout some cells
  • Remove clues above and to the left of a grid

Credit

Click here to read another Beyond Injury post in the Torture or Teacher puzzle series.

Thanks to Puzzlewiki for providing examples of some puzzle variations; Google for helping me find the picture; and all the people who, directly or indirectly, made it possible for me to include the picture and text I used in this post.

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