Dominoes | justpuzzles

Dutch puzzle designer Leon Balmaekers contacted me recently and told me he had written some booklets with puzzles for highly gifted children. The booklets are in Dutch, and contain a variety of puzzles. The highly gifted children in a classroom can make some of these puzzles when they have completed the normal exercises in a breeze.

One of the puzzle types uses a normal 0-6 domino set. Look at the figure in problem 1. In contrast to dominosa, the domino puzzle type most often used, the borders are clear, but the digits are missing.

Problem 1.^**/*****
Domino_laydown_1_exercise
The numbers along the sides are the sum of the pips in the respective rows and columns. It is up to you to figure out which domino should go where. Normal domino rules are followed: whenever two bones lay end to end, the numbers are equal.

For your convenience, here is a complete double 6 set:
Domino_double_6_set

You can check your solution here

Problem 2^**/*****
Domino_laydown_2_exercise

You can check your solution here

Problem 3^***/*****
Domino_laydown_3_exercise

You can check your solution here

A new puzzle is published at least once a month on the first Friday of the month. Additional puzzles may be published on other Fridays.

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)