Triangular Dominoes

Last updated

Triangular Dominoes is a variant of dominoes using equilateral triangle tiles, patented by Franklin H. Richards in 1885. Two versions were made: a starter set of 35 unique tiles, with each side numbered from zero to four pips, and an advanced set of 56 unique tiles, with each side numbered from zero to five pips. In both versions, a wild card "boss" tile was included, making 36 and 57 tiles in each complete set, respectively.

Contents

Equipment

In his patent, Richards used a three-digit notation, referring to the pips in clockwise order from the side(s) with the lowest value. Richards illustrated the tiles as two unique sets, with pip values subject to the following restrictions: [1]

In addition to this marking scheme, Richards added the sum of all pips to the center of the tile. [1]

Richards Triangular Domino sets
TriplesDoublesSingles
TriDominoes Richards 000.svg TriDominoes Richards 001.svg TriDominoes Richards 002.svg TriDominoes Richards 003.svg TriDominoes Richards 004.svg TriDominoes Richards 005.svg
000001002003004005
TriDominoes Richards 111.svg TriDominoes Richards 011.svg TriDominoes Richards 112.svg TriDominoes Richards 113.svg TriDominoes Richards 114.svg TriDominoes Richards 115.svg   TriDominoes Richards 021.svg TriDominoes Richards 031.svg TriDominoes Richards 041.svg TriDominoes Richards 051.svg  
111011112113114115012013014015
TriDominoes Richards 222.svg TriDominoes Richards 022.svg TriDominoes Richards 122.svg TriDominoes Richards 223.svg TriDominoes Richards 224.svg TriDominoes Richards 225.svg TriDominoes Richards 032.svg TriDominoes Richards 042.svg TriDominoes Richards 052.svg TriDominoes Richards 132.svg TriDominoes Richards 142.svg TriDominoes Richards 152.svg
222022122223224225023024025123124125
TriDominoes Richards 333.svg TriDominoes Richards 033.svg TriDominoes Richards 133.svg TriDominoes Richards 233.svg TriDominoes Richards 334.svg TriDominoes Richards 335.svg TriDominoes Richards 043.svg TriDominoes Richards 053.svg TriDominoes Richards 143.svg TriDominoes Richards 153.svg TriDominoes Richards 243.svg TriDominoes Richards 253.svg
333033133233334335034035134135234235
TriDominoes Richards 444.svg TriDominoes Richards 044.svg TriDominoes Richards 144.svg TriDominoes Richards 244.svg TriDominoes Richards 344.svg TriDominoes Richards 445.svg   TriDominoes Richards 054.svg TriDominoes Richards 154.svg TriDominoes Richards 254.svg TriDominoes Richards 354.svg  
444044144244344445045145245345
TriDominoes Richards 555.svg TriDominoes Richards 055.svg TriDominoes Richards 155.svg TriDominoes Richards 255.svg TriDominoes Richards 355.svg TriDominoes Richards 455.svg
555055155255355455

Percy Alexander MacMahon showed there were 24 possible combinations when each of the three edges of an equilateral triangle are assigned one of four values, and showed the number of unique pieces that can be made in this way is for unique values. [2] :2 For , there are 45 unique combinations possible, and for , there are 76 unique combinations; the reduced set of 35 and 56 in Triangular Dominoes, for 0–4 and 0–5 pips, respectively, result from the additional restriction for increasing values around each side of the tiles when counting clockwise. This can be demonstrated by examination of the "singles" tiles: where 012 is a valid sequence in Triangular Dominoes, 021 is not, and so the mirror image of each "singles" pattern is excluded; there are ten excluded patterns for the set of 0–4 pips and twenty for the set of 0–5 pips. By examination, mirror images of the triples and doubles are identical to the original tiles and so these patterns already adhere to the counting-up restriction.

These restrictions and resulting tile set of Triangular Dominoes were retained, with markings moved to the corners using Arabic numerals for Triominoes , which was published in 1965.

Gameplay

"Boss" wild card tile TriDominoes Richards boss.svg
"Boss" wild card tile

Richards proposed several games that could be played in the patent. [1]

Points

For this variant, the "boss" tile may be included or left out. The tiles are distributed evenly between the players. Play is led by the player holding the highest triple tile. Each player takes a turn, placing one tile on the table; each tile must be added next to the tile that was placed in the preceding turn, matching the number of pips on adjacent sides. Once one player exhausts their hand, the game is over and the winner's score is determined by the sum of the pips on the tiles remaining in their opponents' hands. [1]

Muggins

This variant is similar to "points", except the matching criterion is the sum of pips on adjacent sides must be a multiple of five. [1]

Star

This variant allows players to lay tiles side-to-side or corner-to-corner. Corner-to-corner plays are allowed when the player is able to match the number on both sides of the corner. If a corner-to-corner match is created, that player can take another turn. Scoring in this variant is accomplished when the sum of all the pips on both dominoes (whether matched side-to-side or corner-to-corner) is a multiple of five; [1] for example, if the 233 and 334 tiles are laid next to each other, the total sum is (2+3+3)+(3+3+4)=18, not divisible by five and hence no score is awarded. Alternatively, if the 233 and 133 tiles are laid next to each other, the total sum is 15, divisible by five, and the player is awarded 15 points.

When the "boss" tile is played, the tile is assumed to have enough pips to bring the sum of it and adjacent tile(s) to a multiple of five. Subsequent tiles played next to the "boss" tile assume the value is zero. [1]

Related Research Articles

<span class="mw-page-title-main">Chinese dominoes</span> Type of dominoes

Chinese dominoes are used in several tile-based games, namely, tien gow, pai gow, tiu u and kap tai shap. In Cantonese they are called gwāt pái (骨牌), which literally means "bone tiles"; it is also the name of a northern Chinese game, where the rules are quite different from the southern Chinese version of tien gow.

<span class="mw-page-title-main">Dominoes</span> Chinese and European game played with rectangular tiles

Dominoes is a family of tile-based games played with gaming pieces. Each domino is a rectangular tile, usually with a line dividing its face into two square ends. Each end is marked with a number of spots or is blank. The backs of the tiles in a set are indistinguishable, either blank or having some common design. The gaming pieces make up a domino set, sometimes called a deck or pack. The traditional European domino set consists of 28 tiles, also known as pieces, bones, rocks, stones, men, cards or just dominoes, featuring all combinations of spot counts between zero and six. A domino set is a generic gaming device, similar to playing cards or dice, in that a variety of games can be played with a set. Another form of entertainment using domino pieces is the practice of domino toppling.

<span class="mw-page-title-main">Pai gow</span> Chinese gambling game using tiles

Pai gow is a Chinese gambling game, played with a set of 32 Chinese dominoes. It is played in major casinos in China ; the United States ; Canada ; Australia; and New Zealand.

Pips are small but easily countable items, such as the dots on dominoes and dice, or the symbols on a playing card that denote its suit and value.

<span class="mw-page-title-main">Snub cube</span> Archimedean solid with 38 faces

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.

<span class="mw-page-title-main">Triominoes</span> A board game consisting of triangular tiles.

Triominoes is a variant of dominoes using triangular tiles published in 1965. A popular version of this game is marketed as Tri-Ominos by the Pressman Toy Corp.

10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

<span class="mw-page-title-main">Wallpaper group</span> Classification of a two-dimensional repetitive pattern

A wallpaper is a mathematical object covering a whole Euclidean plane by repeating a motif indefinitely, in manner that certain isometries keep the drawing unchanged. For each wallpaper there corresponds a group of congruent transformations, with function composition as the group operation. Thus, a wallpaper group is a mathematical classification of a two‑dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tessellations, tiles and physical wallpaper.

<span class="mw-page-title-main">Shut the box</span> Game of dice

Shut the box is a game of dice for one or more players, commonly played in a group of two to four for stakes. Traditionally, a counting box is used with tiles numbered 1 to 9 where each can be covered with a hinged or sliding mechanism, though the game can be played with only a pair of dice, pen, and paper. Variations exist where the box has 10 or 12 tiles.

<span class="mw-page-title-main">42 (dominoes)</span> Trick-taking dominoes game

42, also known as Texas 42, is a trick-taking game played with a standard set of double six dominoes. 42 is often referred to as the "state game of Texas". Tournaments are held in many towns, and the State Championship tournament is held annually in Hallettsville, Texas on the first Saturday of March each year. In 2011 it was designated the official State Domino Game of Texas.

<span class="mw-page-title-main">Muggins</span> Domino game

Muggins, sometimes also called All Fives, is a domino game played with any of the commonly available sets. Although suitable for up to four players, Muggins is described by John McLeod as "a good, quick two player game".

<span class="mw-page-title-main">Mexican Train</span> Domino board game

Mexican Train is a game played with dominoes. The object of the game is for a player to play all the tiles from his or her hand onto one or more chains, or trains, emanating from a central hub or "station". The game's most popular name comes from a special optional train that belongs to all players. However, the game can be played without the Mexican train; such variants are generally called "private trains" or "domino trains". It is related to the game Chicken Foot.

In mathematics, the Schröder number also called a large Schröder number or big Schröder number, describes the number of lattice paths from the southwest corner of an grid to the northeast corner using only single steps north, northeast, or east, that do not rise above the SW–NE diagonal.

<span class="mw-page-title-main">Penrose tiling</span> Non-periodic tiling of the plane

A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s.

Serpentiles is the name coined by Kurt N. Van Ness for the hexagonal tiles used in various edge-matching puzzle connection abstract strategy games, such as Psyche-Paths, Kaliko, and Tantrix. For each tile, one to three colors are used to draw paths linking the six sides together in various configurations. Each side is connected to another side by a specific path route and color. Gameplay generally proceeds so that players take turns laying down tiles. During each turn, a tile is laid adjacent to existing tiles so that colored paths are contiguous across tile edges.

<span class="mw-page-title-main">Glossary of domino terms</span> List of definitions of terms and jargon used in dominoes

The following is a glossary of terms used in dominoes. Besides the terms listed here, there are numerous regional or local slang terms. Terms in this glossary should not be game-specific, i.e. specific to one particular version of dominoes, but apply to a wide range of domino games. For glossaries that relate primarily to one game or family of similar games, see the relevant article.

<span class="mw-page-title-main">MacMahon Squares</span> Puzzle published in 1921 by Percy MacMahon

MacMahon Squares are an edge-matching puzzle first published by Percy MacMahon in 1921, using 24 unique squares with 3-color patterns; each of the four edges is assigned a single color. The complete set of 24 squares are organized next to each other by matching edge colors to create a 4 by 6 grid. Such tessellation puzzles have multiple variants, which are determined by restrictions on how to arrange the 24 squares. This game has also been commercialized in numerous physical forms, by various companies.

Le Trioker is an corner-matching puzzle game played using 25 equilateral triangle-shaped tiles. Each corner is marked with zero, one, two, or three dots and newly placed pieces must match the values on pieces already placed on the game board, similar to the gameplay of the earlier Triominoes.

References

  1. 1 2 3 4 5 6 7 US 331652A,Franklin H. Richards,"Domino",published December 1, 1885
  2. MacMahon, P. A. (1921). New Mathematical Pastimes. Cambridge University Press. Retrieved 19 December 2023.