How to Solve Domino Hunt Puzzles
O.S. Adler originally invented a puzzled called Dominosa in 1874, combining the word “domino” with his initials. Other names over the years have included “dominosa omnibus”, “solitaire dominoes”, “deductomino”, “domino search”, “domino system,” and now Domino Hunt.
From a grid of numbers, find all the dominoes in a given set. The grid may consist of normal digits or patterns of dots like in our example puzzle. The goal is to figure out where all unique pairs of numbers are in the grid, and wall them off as individual dominoes.
Rules
- Most of the time, you are told which set of dominoes are used. In our example, we will use double-4s, which include every combination from 0-0 through 4-4. Some puzzles may simply tell you to find every unique pairing, and determining the individual options is up to you.
- Use every possible combination of numbers.
- You may not use any pairing more than once.
Basic Techniques to Solve
- Use corners to help eliminate duplicates.
- Check walls to find dominoes that MUST be a certain orientation.
- Mark off unique pairings.
- Keep a list of possible combinations.
- Don’t create regions with an odd number of digits.
- Trial and error.
Using Corners
Whenever you have number in a corner that has the same number in both possible directions, you know that that domino must be in one of those two places, so it can’t exist anywhere else in the puzzle. This means you can place a wall between all of the places that number pair exists, except for the corner.
Sometimes, you might wall off a number on the top and bottom, or the left and right. Now, it only has two exit points, so if those numbers are the same, you can also treat it as a “corner,” even though the two options are in a straight line.
Forced Dominoes
When you wall off a number on three sides, the remaining number must be the one it is paired with, so you can mark that domino.
Unique Dominoes
In more complex puzzles, you may find yourself having to carefully go through the grid and look for pairings that only occur once. Typically, doubles will be the easiest to spot, but if you get stuck following the first two tips, this is your next fallback to get moving again.
Keep a List
If the puzzle only gives you the grid, it may be helpful to write out the possible combinations, or draw a simple diagram. Use this to keep track of what pairs are left, especially in more difficult puzzles. For example, here are the dominoes we’ve solved so far.
More importantly, when you are certain of a domino location in the grid, draw lines between every other pairing of those numbers. This makes it more clear where domino borders are as you hunt.
No Odd Regions
You can tell if a domino placement is invalid if it blocks an area of the grid with an odd number of spaces. Dominoes are always pairs of numbers, so every region that can contain a group of dominoes must have an even total of numbers. For example, If we place these two dominoes marked in gray, you will not be able to place dominoes that dover the 5 spaces in the purple region.
Trial and Error
You can solve most puzzles with the tips above, but sometimes you might find yourself stuck. If you find yourself needing to guess, the best method is to choose a corner, and pick one of the placement options. You want to do this where it creates a forced domino. Now, follow the chain reaction of solvable dominoes until you reach an invalid option (or solve the puzzle). Once you know a sequence results in an illegal placement, you can eliminate the initial possibility you chose.
Solving the Puzzle
Now that we’ve seen examples of the basic strategies, let’s go ahead and solve the rest of our sample Domino Hunt puzzle.
