Serpentiles
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.
Serpentiles is also the name of a single-player puzzle connection game developed by Brett J. Gilbert and published by ThinkFun in 2008.
[2] There are five distinct combinations of six sides and three paths,[3] ignoring for now the possibility of changing path color: An orthogonal rotation that leaves the hexagon in the same orientation (with flat sides to the left and right) is 60°.
To uniquely describe each rotational position, imagine a reference frame is applied where each side is numbered from 1 to 6 sequentially anti-clockwise.
A single orthogonal rotation of the shape will add one (if anti-clockwise) or subtract one (if clockwise) to each number, modulo 6.
The orientation of the reference frame (clockwise or anti-clockwise) only affects the arithmetic required to rotate the tile.
Describing the tiles by linked sides also implicitly includes the three-digit Van Ness notation.
For any arbitrary three-pair sequence AB-CD-EF, the Van Ness notation can be recovered by the following formula:
The square with two paths linking sides can be described in a similar fashion, using a two-digit notation yz; there are just two potential configurations.
[3] Like the hexagonal case, 20 (where all paths link opposite sides) has rotational symmetry.
There are 18 distinct combinations:[3] As with the preceding hexagon and square examples, the case linking all the opposite sides (4000) has rotational symmetry.
Note that for the octagon, the notation no longer uniquely describes the path configuration.
The rotational position notation can be applied to distinguish these tiles; with a reference frame numbered anti-clockwise starting from the bottom edge, 0121(a) above can be written as "0121 12-36-47-68", which is distinct from 0121(b): "0121 12-38-46-57".
For example, a regular 3-sided polygon (equilateral triangle) could have 2 entry points per side.
[3] Although the Van Ness notation can be applied by modifying it to count adjacency rather than sides, each tile is not uniquely described by the Van Ness notation, although the relationship between the 003(a) and (b) cases can be seen by inscribing a triangle, as the example shown here.
Similarly, a regular 4-sided polygon (square) with 2 entry points per side has 35 potential combinations using 4 paths per tile.
This set of four-sided polygons with two entry points per side and four paths per tile is used in the commercial board game Tsuro.
For the general case where the tiles are n-sided regular polygons with m entry points per side so the product
[3] (Many of the values from the original source are listed as N/C, meaning not computed)[3] A game of Psyche-Paths requires one to six players.
Six blank tiles are provided as "wild cards" and are considered to continue any adjacent path.
If the player is unable to play the tile or makes an illegal play, it is retained and the player is penalized a number of points equal to the number of paths running through the retained tile at the end of the game.
[7] In "Standard" Psyche-Paths, two to four players each draw a hand of six tiles at the start of the game.
When laying down tiles, points are awarded only when two or more ends of an existing path is connected.
[7] "Solitaire" Psyche-Paths does not have specific rules, but rather suggestions, such as building alternating rows of eight and nine pieces in length using legal moves.
[8][9] The Serpentiles (2008) game was developed by Brett J. Gilbert[10] and published by ThinkFun in 2008.
[12] The original hex-tile edge-matching connection game, Psyche-Paths, was designed by Charles Titus and Craige Schensted and published in the 1960s[13] with the 85 unique tile combinations and 6 blank "wild cards" on cardboard tiles.
[7] In a review, researchers noted the game "accommodates a wide variety of ages, interests, and playing styles ... [involving] a number of skills that are of special interest to teachers and parents.
[15] Tantrix was released in 1988 by inventor Mike McManaway using four of the five possible path combinations (using Van Ness's notation: 003, 021, 102, and 120, excluding 300) to create 56 unique tiles, each with three different colors chosen from a palette of four.
The primary innovation of Tantrix is the encoding of numbers on the reverse side of the tiles, allowing subsets of the 56 to be used for solitary puzzles.
Tantrix uses the subset of tiles with three different path colors exclusively, and excludes the 300 Triple Cross series.
