What is Domino?
I won't go into details now. I shall describe puzzles with dominos and
then only with all its 28 pieces.
||Domino is a famous game with domino pieces (shorter dominos).
Two or more players must alternately lay fitting pieces. The winner is
the person who gets rid of all his pieces first.
Here you see a picture of the first phase of the play.
Domino Pieces top
Two squares form a domino (above on the right). So you get 1+2+3+4+5+6+7=28
You need eight sequences of seven squares for the pieces (down left).
Altogether there are 56 squares. They show the numbers 0 to 6. The numbers
are represented by patterns you find on dice. An empty square takes the
place of the number 0.
Figures from Dominos top
Laying figures is a popular activity with dominos. Dominos with the
same number of points must meet like with the normal domino game. - You
usually limit to symmetrical patterns.
||You can easily make a square framework 15x15 from all dominos.
2nd and 3rd examples: Symmetrical figures with
axis and centre point
You should lay the crossings first. There you need 3 squares with the same
number of points. Therefore you must use dominos with the same number of
points also for another crossing, because there are 6*2 squares altogether.
4th example: A symmetrical figures with one axis
5th example: Symmetrical figures with a centre
point (Book 2 or book 3) top
||This is a well-known figure, which you can form with all the 28 dominos.
You get more patterns, if you reflect the figure, or, this is more interesting,
if you permutate the numbers of points on the dominos. You can replace
the squares (0,1,2,3,4,5,6) by the squares (3,5,1,0,6,2,4) for example.
||Quadrilles go back to the French mathematician Edouard Lucas
(1842-1891). Those are compact figures with all 28 dominos. 2x2squares
with the same numbers of points are included in. Here is an example.
Seven Squares top
You can lay seven square frames with all the 28 dominos. Dominos with the
same number of points meet.
You can lay seven square frames with all the 28 dominos, so that the sums
of the numbers of points are the same at all four sides (book 1).
The simple square frame 15x15 from the top also has the feature of the
same sum at all four sides. The sum is (1+2+3+4+5+6)*8/4 = 44.
Making pairs top
Tip: You should find the dominos with the same number
||You give a 7-8-matrix with the numbers 0 to 6, each number eight times.
These are the squares, which the dominos have.
The problem is to assemble two squares lying underneath the other or
side by side.
This is a solution.
You can invent this kind of puzzle yourself.
Dominos on the Internet top
James Masters (tradgames.org.uk)
Leonid Mochalov [PUZZLES of LEONID MOCHALOV]
Puzzles with Dominoes
(translated to English)
(1) Walter Sperling: Auf du und du mit Zahlen, Rüschlikon-Zürich
(2) Pieter van Delft, Jack Botermans: Denkspiele der Welt, München
(3) Karl-Heinz Koch: ...lege Spiele, Köln 1987 (dumont taschenbuch1480)
(4) Martin Gardner: Mathematischer Zirkus, Frankfurt a.M. 1988
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