4
$\begingroup$

So I've been working on a set of domino puzzles, I call DominoBrane recently, it's sort of similar to Dominosa - except that, unlike Dominosa, the rules of the normal domino game must be followed.

  • Each domino must connect, as in the normal game, to it's neighbour [0:3][3:3][3:5] etc and make a full circuit of all the 6-dominoes.

  • At each square, there must be no ambiguity as to which is the connected domino (eg, for a 4 there will be only one adjacent domino with a 4)

  • The dominoes must be constrained to a 7x8 grid.

Here is an example.

╔═══╦═══════╦═══╦═══╦═══════╗
║ 5 ║ 5   4 ║ 4 ║ 3 ║ 3   1 ║
║   ╠═══════╣   ║   ╠═══════╣
║ 6 ║ 0   2 ║ 2 ║ 3 ║ 1   1 ║
╠═══╬═══════╬═══╩═══╬═══════╣
║ 6 ║ 0   0 ║ 0   3 ║ 1   2 ║
║   ╠═══════╬═══════╬═══╦═══╣
║ 4 ║ 1   6 ║ 6   6 ║ 6 ║ 2 ║
╠═══╬═══╦═══╬═══════╣   ║   ║
║ 4 ║ 1 ║ 4 ║ 4   4 ║ 2 ║ 5 ║
║   ║   ║   ╠═══╦═══╬═══╬═══╣
║ 1 ║ 0 ║ 3 ║ 3 ║ 4 ║ 2 ║ 5 ║
╠═══╬═══╩═══╣   ║   ║   ║   ║
║ 1 ║ 0   6 ║ 6 ║ 0 ║ 2 ║ 3 ║
║   ╠═══════╬═══╩═══╬═══╩═══╣
║ 5 ║ 5   5 ║ 5   0 ║ 2   3 ║
╚═══╩═══════╩═══════╩═══════╝

And here it is again, showing the path of the chain.

╔═══╦═══════╦═══╦═══╦═══════╗
║ 5 - 5   4 - 4 ║ 3 - 3   1 ║
║   ╠═══════╣   ║   ╠═════|═╣
║ 6 ║ 0   2 - 2 ║ 3 ║ 1   1 ║
╠═|═╬═|═════╬═══╩═|═╬═|═════╣
║ 6 ║ 0   0 - 0   3 ║ 1   2 ║
║   ╠═══════╬═══════╬═══╦═|═╣
║ 4 ║ 1   6 - 6   6 - 6 ║ 2 ║
╠═|═╬═|═╦═══╬═══════╣   ║   ║
║ 4 ║ 1 ║ 4 - 4   4 ║ 2 ║ 5 ║
║   ║   ║   ╠═══╦═|═╬═|═╬═|═╣
║ 1 ║ 0 ║ 3 - 3 ║ 4 ║ 2 ║ 5 ║
╠═|═╬═|═╩═══╣   ║   ║   ║   ║
║ 1 ║ 0   6 - 6 ║ 0 ║ 2 ║ 3 ║
║   ╠═══════╬═══╩═|═╬═|═╩═|═╣
║ 5 - 5   5 - 5   0 ║ 2   3 ║
╚═══╩═══════╩═══════╩═══════╝

So here's the puzzle: 6-DominoBrane #1, first published here

Following the rules above, find the solution where the numbers match the grid as follows (a blank means 'any number':

╔═══╦═══╦═══╦═══╦═══╦═══╦═══╗
║ 0 ║   ║   ║ 0 ║   ║   ║ 0 ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║   ║ 1 ║   ║ 1 ║   ║ 1 ║   ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║ 3 ║   ║ 2 ║ 2 ║ 2 ║   ║ 4 ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║   ║ 6 ║   ║ 3 ║   ║ 3 ║   ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║ 3 ║   ║ 4 ║ 3 ║ 4 ║   ║ 5 ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║   ║ 5 ║   ║ 2 ║   ║ 5 ║   ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║ 6 ║   ║ 4 ║ 1 ║ 1 ║   ║ 6 ║
╠═══╬═══╬═══╬═══╬═══╬═══╬═══╣
║   ║ 6 ║   ║ 0 ║   ║ 2 ║   ║
╚═══╩═══╩═══╩═══╩═══╩═══╩═══╝

If you solve it, I would really love to know how!
You will be the first person to solve any 6-DominoBrane.

There is exactly one solution to this puzzle.

Be careful to make sure that each square is unambiguous as to where it would go next - the problem is much easier without that constraint.

(Kudos to @bobble for telling me I need to provide single solution puzzles)

$\endgroup$
4
  • 1
    $\begingroup$ I've added [grid-deduction] and [logical-deduction], but they don't fully fit. The general expectation is that there is only 1 solution, which can be unambiguously deduced using only logic. Multiple solutions is seen by some here as a mark of a poorly constructed puzzle. Finally, your last question - determining a "hardness" level - is opinion-based and as such I've edited it out. $\endgroup$ – bobble Mar 17 at 0:30
  • $\begingroup$ @bobble, thanks. I'm trying to find a puzzle which guarantees a single solution, while not just becoming a Dominosa puzzle, but that's stumped me! $\endgroup$ – Konchog Mar 17 at 0:36
  • 1
    $\begingroup$ In that case I'd suggest getting more familiar with the unique deductions of this genre. Deusovi has a great guide to creating grid-deductions as well. $\endgroup$ – bobble Mar 17 at 0:38
  • 1
    $\begingroup$ @bobble, thanks for the advice - I have amended the puzzle to provide a unique solution. I was thinking about it the wrong way around! $\endgroup$ – Konchog Mar 17 at 1:18
3
$\begingroup$

Step 1:

Each digit must appear 8 times and connect to itself. Use this to fill in every location where each digit can occur.
enter image description here

Step 2:

Select an arbitrary direction for the dominoes to connect in. We will say the white end connects to the gray end.
enter image description here

Step 3:

Some simple deductions.
The 4 can be filled in because it is necessary for the chain of length 4. enter image description here

Step 4:

To ensure the 02, 03, 04, and 06 dominoes exist, the domino chain must run against the edge.
enter image description here

Step 5:

The chain must tun clockwise around the outer edge.
enter image description here

Step 6:

The 00 and 33 dominoes can now be filled in.
enter image description here

Step 7:

This allows some more deductions.
enter image description here

Step 8:

The 25 domino can only be in one location.
enter image description here

Step 9:

This allows a long chain of deductions.
enter image description here

Step 10:

Fill in the missing dominoes.
enter image description here

$\endgroup$
1
  • $\begingroup$ Absolutely stunning victory! I hope you enjoyed it! $\endgroup$ – Konchog Apr 9 at 8:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.