Trioker

Last updated

Le Trioker is a 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.

Contents

History

Fig.5 from New Mathematical Pastimes (MacMahon, 1921) MacMahon game.svg
Fig.5 from New Mathematical Pastimes (MacMahon, 1921)

In the 1921 book New Mathematical Pastimes, Percy Alexander MacMahon showed there were 24 possible combinations when each of the three edges of an equilateral triangle are assigned one of four colors. [1] :2 In general, the number of unique pieces that can be made in this way is and so for there are 24 unique combinations possible. [1] :3 [2] :225 MacMahon suggested an edge-matching puzzle game could be played with these pieces on a regular hexagonal board, constraining colors to match on adjacent edges and on the borders of the board itself. [1] :4–6 The similar square tiles proposed by MacMahon in the same book have since been adopted into several commercial games.

MacMahon triangular tiles (four colors) [1] :Fig.2c
Triples Doubles Singles
MacMahon d111.svg MacMahon d112.svg MacMahon d113.svg MacMahon d114.svg MacMahon d123.svg MacMahon d132.svg
111112113114123132
MacMahon d222.svg MacMahon d223.svg MacMahon d224.svg MacMahon d221.svg MacMahon d234.svg MacMahon d243.svg
222223224221234243
MacMahon d333.svg MacMahon d334.svg MacMahon d331.svg MacMahon d332.svg MacMahon d341.svg MacMahon d314.svg
333334331 [133]332 [233]341 [134]314 [143]
MacMahon d444.svg MacMahon d441.svg MacMahon d442.svg MacMahon d443.svg MacMahon d412.svg MacMahon d421.svg
444441 [144]442 [244]443 [344]412 [124]421 [142]

The notation used here for the MacMahon equilateral triangular tiles is a simple enumeration of each edge, in anti-clockwise order, starting from the bottom left edge. Rotating each tile by 120° may change this notation (e.g., after rotating the 314 tile, the revised notation would become 431 and 143 in turn) but the actual tile itself remains physically unchanged regardless of its orientation; in other words, these tiles are identical up to rotation despite the change in notation. For consistency, a notation may be adopted in which the count starts from the lowest-numbered edge, proceeding anti-clockwise; in that case, this tile would always be denoted 143. A separate signifier could be used to indicate orientation, for example, the clock hour position of the ones digit, so 143.08 = [314] and 143.04 = [431].

Marc Odier developed the Trioker tiles by shifting the markings from the edges to the corners, [2] :235 as patented and published by Robert Laffont Games in 1969. [3] In addition to the 24 combinations, Odier introduced a tile with a wild card value in one corner, marked by a solid square. [2] :236 Spirou published a supplement in 1970 (with issue 1661), providing the game pieces and a description of how to play it, followed by a regular column through the end of the year. [4]

Trioker tiles
Triples Doubles Singles
Trioker 000-12.svg Trioker 001-12.svg Trioker 002-12.svg Trioker 003-12.svg Trioker 012-12.svg Trioker 021-12.svg
000001002003012021
Trioker 111-12.svg Trioker 112-12.svg Trioker 113-12.svg Trioker 110-12.svg Trioker 123-12.svg Trioker 132-12.svg
111112113110123132
Trioker 222-12.svg Trioker 223-12.svg Trioker 220-12.svg Trioker 221-12.svg Trioker 230-12.svg Trioker 203-12.svg
222223220221230203
Trioker 333-12.svg Trioker 330-12.svg Trioker 331-12.svg Trioker 332-12.svg Trioker 301-12.svg Trioker 310-12.svg
333330331332301310

Like Triominoes, which also use equilateral triangle tiles with values marked in each corner, Trioker requires that adjacent tiles must have matching corners. However, Triominoes are marked from zero to five (or more) and have an additional marking restriction that values may not decrease when counted in a clockwise direction from the lowest value(s), so there are pieces in common between the two games, but neither game is a subset of the other.

Gameplay

Additional tile with "wild card" square symbol Trioker 12W-12.svg
Additional tile with "wild card" square symbol

Le Trioker can be played either as a competitive dominoes-like game against one or more opponents, or as a puzzle game to fill a shape.

General

All variants of the game require the corners of any newly-placed tile to match the corners of adjacent tile(s) that are already on the board, consistent with the placement rule of triominoes. For the competitive variants, the winner is the first to place all their tiles on the board. [5]

Original

Original competitive variant board (1970) Trioker board (original).svg
Original competitive variant board (1970)

The original competitive version of the game published in 1970 used an irregular seven-sided board shaped like a truncated triangle with several marked spaces that require an additional action when a tile is played in that space: [6]

Sid Sackson's holographic notes omit the F5 space. [6] This version uses the full 25-tile set [6] along with red and black "coin" pieces, with the red coins worth 5 and the black coins worth 2.

Rapid

"Rapid" variant board Trioker board (rapid) opt.svg
"Rapid" variant board

The rapid version of the game is intended for two, three, or four players, with each player receiving the following equipment prior to starting:

Rapid setup [7]
PlayersTilesRed coinsBlack coinsRemaining tiles in bank
(after initial draw)
210555
37554
46451

The players draw from the full 25-tile set; red coins are worth 5 points and the black coins are worth 2. Each player hides their triangular tiles. The remaining tiles and coins are held for common use in the bank. [7]

The rapid variant board is an irregular ten-sided shape, taking the form of an irregular hexagon with two indented corners; similar to the original (1970) version, certain spaces are marked with additional actions that are taken when a tile is played in them: [7]

Play starts with the player holding the triple-three ('333') tile; that player places that tile in the "GO" spot, and the next turn proceeds to the player on their left (clockwise). If the '333' tile is not held, the player holding the tile with the largest sum of pips (e.g., '332' = 8; '331' or '322' = 7; etc.) uses that tile to start instead. [7]

The next player must play a tile from their hand that can be placed legally adjacent to the starting tile. If a player does not have a tile that can be placed legally, they must draw one of the remaining tiles from the bank, then either play the drawn tile or pass their turn. When there are no free tiles left in the bank, players must pass instead. [7]

Scoring

After one player empties their hand, that player receives ten points from the bank, while the other players must pay the bank two points plus the sum of the pips on each tile. For example, a player with the '000' tile will pay a total of two points to the bank for that tile, while a player with the '230' tile will pay a total of seven points to the bank (2+[2+3+0]). Because of this, it is advantageous to use higher-value tiles early in the game. [7] The overall winner is the player with the most points. [7]

The game also may end in a draw if no player is able to empty their hand. In that case, the game should be replayed with a fresh draw. [7]

Even-Odd

"Even-Odd" variant board Trioker board (pair-impair).svg
"Even-Odd" variant board

The even-odd version is an advanced variant intended for two players that uses a 24-tile subset, omitting the "joker" piece. One player takes the 12 "even" pieces, while the other player takes the 12 "odd" pieces. Throughout the game, each player's pieces are kept face-up so the opposing player knows which pieces are remaining. [7] Comic characters from Spirou  [ fr ] were assigned to each piece in the version of the game reprinted in that magazine. [8] [9]

Pair-Impair setup
 Pair (Even) Impair (Odd)
Triples Trioker 000-12.svg Trioker 222-12.svg Trioker 111-12.svg Trioker 333-12.svg
000
Bobo
222
Kroston  [ fr ]
111
Sibylline
333
Schtroumpf
Doubles Trioker 001-12.svg Trioker 002-12.svg Trioker 003-12.svg
001
Marc Lebut  [ fr ]
002
Foufi
003
Sophie
Trioker 110-12.svg Trioker 112-12.svg Trioker 113-12.svg
110
Sandy  [ fr ]
112
Vieux Nick
113
Oncle Paul
Trioker 220-12.svg Trioker 223-12.svg Trioker 221-12.svg
220
Patate
223
Benoît Brisefer
221
Timour  [ fr ]
Trioker 332-12.svg Trioker 330-12.svg Trioker 331-12.svg
332
Gil Jourdan
330
César  [ fr ]
331
Attila
Singles Trioker 012-12.svg Trioker 132-12.svg Trioker 021-12.svg Trioker 123-12.svg
012
Tif
132
Bill
021
Tondu
123
Boule
Trioker 230-12.svg Trioker 310-12.svg Trioker 203-12.svg Trioker 301-12.svg
230
Johan
310
Fantasio
203
Pirlouit
301
Spirou

The board has 73 triangular cells arranged in an irregular hexagon. Advanced players may choose to reduce this to a 52-cell board by mutual agreement to avoid the shaded cells, which increases the difficulty. [7]

One of the two players flips a coin, which determines whether they will play the "even" (by flipping tails) or "odd" (heads) side. The even player places the first piece in the center of the board; they may choose any piece they hold, aside from the two triples ('000' or '222'), [7] as that would unfairly limit the opening move for the odd player. The players take turns placing tiles adjacent to placed tiles, observing the corner-matching rules. [7]

When a player completes a hexagon by adding a sixth tile using a legal placement, that player takes another turn immediately. This also applies if two hexagons are completed by a single tile, in which case that player is awarded two more turns. [7]

A player may choose to block their opponent by making it impossible to place one of their remaining pieces legally, which is facilitated by both players keeping the pieces face-up. If there are no legal moves for a player, that player is forced to pass their turn. However, if a player passes and their opponent notices they have a legal move available, the passing player is obligated to place that tile. [7]

The winner is the first player to place their last tile. If there are no legal moves for both players, the winner is the player with fewer tiles remaining; if both players have the same number of tiles, the game is a draw and should be replayed, switching the even and odd roles. [7]

Simple

In Surprenants triangles (1976), Odier proposes several simple game variants, including single, double, and triple linear paths starting from the triple-three tile. [10]

Puzzles

The puzzle variant is intended for solo players to fill a shape while observing corner-matching rules for adjacent tiles. There are many possible shapes, and at least one book has been published with additional shapes beyond those contained in the rulebook. [5]

Related Research Articles

<i>Acquire</i> Business themed board game

Acquire is a board game published by 3M in 1964 that involves multi-player mergers and acquisitions. It was one of the most popular games in the 3M Bookshelf games series published in the 1960s, and the only one still published in the United States.

<span class="mw-page-title-main">Hexagon</span> Shape with six sides

In geometry, a hexagon is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

A polyiamond is a polyform whose base form is an equilateral triangle. The word polyiamond is a back-formation from diamond, because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial 'di-' looks like a Greek prefix meaning 'two-'. The name was suggested by recreational mathematics writer Thomas H. O'Beirne in New Scientist 1961 number 1, page 164.

<span class="mw-page-title-main">Kensington (game)</span> 2-player abstract strategy board game

Kensington is an abstract strategy board game devised by Brian Taylor and Peter Forbes in 1979, named after London's Kensington Gardens, which contains the mosaic upon which the gameboard is patterned. It is played on a geometrical board based on the rhombitrihexagonal tiling pattern. The objective of the game is to capture a hexagon by occupying the six surrounding vertices. The game maintains an elegant simplicity while still allowing for astonishingly complex strategy. The placing and movement of tokens have been compared to nine men's morris.

<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.

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

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, tiles, and wallpaper.

<span class="mw-page-title-main">Escape from Atlantis</span> Board game

Escape from Atlantis is a board game that portrays the sinking of Atlantis and the attempts by the population to escape the sinking island. It was originally released in the United States under the title of Survive! and first published in the English language by Parker Brothers in 1982. The game was invented by Julian Courtland-Smith. Early copies of Escape from Atlantis include the name of the then co-copyright owner, C. Courtland-Smith.

<span class="mw-page-title-main">Hexagonal bipyramid</span> Polyhedron; 2 hexagonal pyramids joined base-to-base

A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices and 18 edges. The 12 faces are identical isosceles triangles.

<span class="mw-page-title-main">Blokus</span> Abstract strategy board game best played with four players

Blokus is an abstract strategy board game for two to four players, where players try to score points by occupying most of the board with pieces of their colour. Similar to jenga, the goal is to leave the other player with no plays. Utilize the different dimensions blocks to fill the board and block out the other players. The board is a square regular grid and the pieces are polyominoes. It was designed by French mathematician Bernard Tavitian and first released in 2000 by Sekkoïa, a French company. It has won several awards, including the Mensa Select award and the 2004 Teacher's Choice Award. In 2009, the game was sold to Mattel.

Skirrid is a board game designed for 2–6 players.

I'm the Boss! is a board game by American designer Sid Sackson. It is a negotiation game in which a group of players compete and cooperate to put together profitable business deals. The goal is to make the most money. I'm the Boss is currently published by Gryphon Games, after the Face2Face Games edition. It was previously published as Kohle, Kies & Knete.

<span class="mw-page-title-main">Eternity puzzle</span> Tiling puzzle

The Eternity puzzle is a tiling puzzle created by Christopher Monckton and launched by the Ertl Company in June 1999. It was marketed as being practically unsolvable, with a £1 million prize on offer for whoever could solve it within four years. The prize was paid out in October 2000 for a winning solution arrived at by two mathematicians from Cambridge. A follow-up prize puzzle called Eternity II was launched in 2007.

Brax is a two-player abstract strategy board game. It was invented in 1889 in America by Frederic B. Denham of New York City. The board design is unique. The players move their pieces along paths on the square board; each path is one of two colors. A piece can move one or two spaces in a turn depending upon whether it matches the color of the path. Players attempt to capture each other's pieces.

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.

Hexagony is an abstract strategy board game for 2 to 6 players that was published as Bin'Fa by Taoist Arts Inc. in 1977, as Hexagony by Avalon Hill in 1980, and later re-released in a slightly modified form by Kenterprises as Bin'Fa.

<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.

Tri-nim is a mathematical abstract strategy game developed by brothers Bruce L. Hicks and Hervey C. Hicks and published by WFF 'N PROOF Games from 1970 to 1975. Players move pieces around a triangular board, attempting to score points by being the last to enter each of the corners. It is a variation on the strategy game Nim.

Domain is a tile-based abstract strategy game first published throughout Europe in 1982. Players place multicoloured polymino tiles on a game board and flip any of their opponent's pieces adjacent to them in order to have the most squares covered by their colour at the end of the game.

<span class="mw-page-title-main">Contack</span> Tabletop game

Contack is a dominoes-like game for one to seven players which was patented by Parker Brothers and published in 1939. It uses 36 equilateral triangle tiles; each side is assigned a different color and numerical value. Players take turns laying tiles from a hand of five next to tiles already on the table; newly-laid tiles must match the color of adjacent tile(s).

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.

References

  1. 1 2 3 4 MacMahon, P. A. (1921). New Mathematical Pastimes. Cambridge University Press. Retrieved 19 December 2023.
  2. 1 2 3 Gardner, Martin (1985). "16: Colored Triangles and Cubes". Mathematical Magic Show . Penguin Books. pp. 223–239. ISBN   978-0-14-007118-4.
  3. "Le Trioker". Escale à jeux. Retrieved 19 December 2023.
  4. "Le journal de Spirou en 1970" [The magazine 'Spirou' in 1970]. BDoubilees.com (in French). Retrieved 26 December 2023.
  5. 1 2 Brassinne, Michel (December 1980). "30 'bons' jeux au banc d'essai" [30 'good' games tested]. Jeux & Stratégie (in French). Excelsior Publications. p.  48 . Retrieved 28 December 2023.
  6. 1 2 3 Sackson, Sid (June 3, 1970). "Wednesday, 3 June 1970". The Sid Sackson Portal. Retrieved 28 December 2023.
  7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 "Le Trioker" (PDF) (in French). Robert Laffont. Retrieved 28 December 2023 via Escale à Jeux.
  8. "F5 (451) ""Le Trioker"" DIY Set - Spirou Supplement No. 1661". eBay. Retrieved 29 December 2023.
  9. "F5 (454) ""Le Trioker"" DIY Set - Spirou Supplement No. 1686". eBay. Retrieved 29 December 2023.
  10. Odier, Marc; Roussel, Yves (1976). "Surprenants triangles". Les distracts. No. 1. CEDIC. ISBN   9782712406011. ISSN   0397-4375 . Retrieved 28 December 2023.