Christmas 2017

Dominosas are puzzles where the dominoes have been shuffled and turned face up. All the numbers are given, but the borders between the dominoes are not given – these have to be solved by the reader.
I used to publish quarterly on them at my site domino plaza.

Usually a 6×6 set of dominoes is used, though larger or smaller sets can be used.

Here are two examples:
1) The christmas bauble^**/*****

2) The church^****/*****

You can check your solution here

3) Solving strategies
a) Counts
Make a count of how often all combinations appear. To do so, list all dominoes and how often they appear in the puzzle:
0-0: 2
1-0: 3
1-1: 5
2-0: 2
2-1: 1
2-2: 3
and so on.
This will give you the position of 2-1. Mark the borders on the printed puzzle.

b) Cross off deleted connections



Continuing the above example, it is easy to jump to a conclusion about 3-3, but before that we have some bookkeeping to do. Identifying the domino severed a number of links. In our example the severed links are the 3-1, 6-1, 2-0, and 5-2. When we update our list above for these severed links, we find that the number of 2-0 combinations is now reduced to 1, giving another domino.

c) Unique positions.



In this diagram, it is easy to see that in the top left position, only-the 3-3 is possible.

d) Block impossible links
Identifying the 3-3 domino blocks the link between all other 3-3 combinations:



This in turn, will in some situations trigger another situation like in step c)

New puzzles are published at least twice a month on Fridays. Solutions are usually published after one or more weeks.

External links:
https://www.puzzle-dominosa.com/ – play them online
https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/dominosa.html – another online game site
http://medmunds.github.io/puzzles/dominosa.html – 3rd in line play
https://play.google.com/store/apps/details?id=com.oxothuk.dominosa – android app
http://www.mathematica-journal.com/2014/10/three-ways-to-solve-domino-grids/ – three ways to solve them.