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Here is another domino puzzle. This is considerably easier than puzzle set earlier this week, and definitely doesn’t need bifurcation.

This uses 4-Dominoes (all the normal dominoes, minus any with a 5 or a 6).

  1. Each domino must connect, as in the normal game, to it's neighbour [0:3][3:3][3:1] etc and make a full circuit of all the 4-dominoes.

  2. For each square in the grid there is exactly one adjacent square which has the same number but is not part of the same domino.

  3. The dominoes must be constrained to a 5x6 grid.

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

The Puzzle: 4-DominoBrane #002 "81",

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

There is exactly one solution to this puzzle.

Some Starters

Corners are gone through only one way.

Following the circuit, numbers always come in exactly 1 run of 4 (where the double is) and exactly 1 run of 2 (where the other two tiles join).

Rule #2 is your friend

Look where some numbers cannot go.

Work on establishing domino edges, chain directions, and numbers.

Even if you cannot yet place their ends, you can work out exactly which pieces will be needed in a sub-chain once there is a double, and that eliminates their use elsewhere.

Just like all other 'missing pieces' grids, start where there's more information!

Tallying the 2-run, the 4-run, and dominoes currently used is pretty important.

The numbers preceding and following the two runs are all different!

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This is one solution, which has not one but two closed circuits.

Here is the solved puzzle:

Revised dominobrane solution

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  • $\begingroup$ Obviously failing rule 1 isn’t a solution - but all the numbers are correct, but your route is wrong! There are two options at column 1 row 4. In fairness, and this is a mistake I made for the puzzle, the two relevant dominoes can also be rotated. Try taking one east instead of one north... $\endgroup$ – Konchog Mar 19 at 19:48
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    $\begingroup$ @Konchog I edited the puzzle to take the correct route. Thank you for the hint. $\endgroup$ – Joe Kerr Mar 19 at 19:55
  • $\begingroup$ Hope you enjoyed it! $\endgroup$ – Konchog Mar 20 at 0:00

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