Permutations – Game components showing all possible combinations of a kind
Daniel Danzer
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I start this with the "28"-siblings Trippples and Ta Yü. You don`t know what these have to do with each other?

Look at this picture:


You see a long oktagon with numbers for each of the eight "directions". Now have a look at these details of a Ta Yü image and a Trippples image:


(Original shots by Joe Casadonte and Terraliptar)

They both represent the combination " 1 - 3 - 6 " from the diagram above.

Now, how many possibilities do you have, combining three directions out of eight possible ones? 28, if you allow turning the pieces. 56, if you don`t. In Trippples you have 56 tiles, one for each possible combination in a fixed orientation (the dot), plus some blank, start and end tiles for the game on a 8 x8 grid.
In Ta Yü, you have 4 times each, allowing turning around, making 112 tiles.

As though gameplay is totally different, they both have this permutation in common!

Now, which other games - not necessarily siblings to others - do you know using complete permutations - all possible combinations of a certain kind - as explicit part of the game components?

Feel free to add! Plus: Maybe you find more "28 / 56" - ones?

I will sort this list in groups, if there are more than one game for other examples.

PLUS Special Question: Any NON-ABSTRACT games using stuff like this?

Edit: I changed the headline until I find an even better one - math definitions drive me crazy sometimes (see comments below) ...
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26. Board Game: Haar Hoolim Perception Games [Average Rating:7.17 Unranked]
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"... a set of 36 cards. Each card is a 2x3 grid with the squares colored in black and gold. All possible patterns are included."

I'm looking for the rules. World cat the global library db tels me "No copies have been found in Australia" and then helpfully directs me to a New York library.
 
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27. Board Game: Nitty Gritty [Average Rating:0.00 Unranked]
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The components of this game puzzle are 2x2 tiles using all possible combinations of three colors. The copy I grew up with was white/blue/green instead.



At some point I read that Multimatch II is functionally identical.
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28. Board Game: PotzKlotz [Average Rating:5.17 Unranked]
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This game has a set of 56 cards. The cards show arrangements of 5 cubes, with the cubes adjacent orthogonally. The arrangements sit on the ground. The cubes can be stacked or spread flat, but always each cube is connected to the group by one, or more, whole cube side/s. Examples of the arrangements on the cards can been seen on pg 4 of
https://www.friedrich-verlag.de/data/E06FDDD1E9C74CBA948EFF1...


A publisher's pdf for teaching materials related to the game (Zeichne Die Linien 1 on third page) shows 28 configurations.
https://www.friedrich-verlag.de/data/9095BE17E653424689A0452...

Many more have been found by geeks.
However it is currently uncertain wherever all stackings are included on the cards.

It is also possible that the 56 cards contain duplicates of some stackings.

 
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29. Board Game: Take it Easy! [Average Rating:6.61 Overall Rank:1452]
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Don't all the games in this family count?
There are 3 colors in each of the 3 directions (2 colors in each of the 4 directions in Take it Higher!) and the tiles show all possible combinations of these.
 
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30. Board Game: Stax [Average Rating:7.04 Unranked]
Néstor Romeral Andrés
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Tiles showing all 13 unique arrangements of pointers to 6 edges (one of them is assymetrical and can be placed any side up).

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31. Board Game: XATS [Average Rating:7.00 Unranked]
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Brother of Stax (above).

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32. Board Game: Osbo [Average Rating:8.00 Unranked]
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All side-centred celtic knot segments in a square.
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33. Board Game: Heptalion [Average Rating:7.40 Unranked]
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28 domino pieces, showing all possible pairs for 7 symbols.

Moreover, each pair is shown on the board exactly three times.

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34. Board Game: RED [Average Rating:7.09 Overall Rank:6866]
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6 possible frame-circle combinations for 3 colours so that the circle colour and the frame colour are different.

(I love this list!)


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35. Board Game: Pilus [Average Rating:7.09 Unranked]
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30 tiles of 4 colours each showing all possible combinations of 5 colours without repetition and discarding rotations.

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36. Board Game: Pentactic [Average Rating:6.73 Unranked]
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12 pentominoes
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37. Board Game: Nestortiles [Average Rating:7.36 Unranked]
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10 colours x 6 numbers = 60 tiles


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38. Board Game: Ahoy [Average Rating:5.95 Overall Rank:8680]
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- 4 pictures in the game.
- On each card at both sides 1 picture.
- Never 2 equal pictures on 1 card.
So 6 combi's: AB / AC / AD / BC / BD / CD.
Each combi is 2 times in the game. So 12 cards in the game.

BTW: When you have an eye for it and take a close look, you can determine the "front" and "back" sides of cards (at the corners mainly). Looking that precise you will see that it has 12 combinations printed, BA/CA/DA/CB/DB/DC too, so all 12 printing combinations are in the game.
 
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39. Board Game: 6th Year Cwali [Average Rating:4.70 Unranked]
Corné van Moorsel
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Per 3D shape each corner of each side has the same degree.
You can make precise 5 possible shapes with that rule: the D4, D6, D8, D12 and D20 in this game.
 
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40. Board Game: Aloha [Average Rating:5.44 Overall Rank:14425]
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- hexagon tiles.
- Each of the 6 corners is land or water.
- In the middle of each tile land or water from the corners are connected.

That makes 22 possible tiles. Each 3 times in the game, so 66 tiles in the game.
In the picture you see 1 set of 22 tiles in 1 punch-out frame.
 
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41. Board Game: Mondriaan 2020 [Average Rating:6.37 Overall Rank:8829]
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- Square tiles.
- Each corner has 1 color.
- 3 colors are in the game.
That makes 24 possible tiles. The blue-blue-blue-blue tile is not in this game, so 23 tiles are in *Mondriaan2020* ... For this list I should write that each tile must have a combination of at least 2 colors. Then 21 tiles are possible and precise in this game. The red and yellow tile don't get mixed in the tiles which get divided over the 2 players with the remaining 1 placed as start tile.
(The curved color shapes are made for holding color connections in the game more clear. That doesnt change the theory here.)
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42. Board Game: Subulata [Average Rating:6.55 Overall Rank:5854]
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Nice one:
- Each tile is a 3x3 spaces square.
- Each space is water, leaf or flower.
- Water is never connected to water at 1 tile, a leaf never to a leaf and a flower never to a flower.
That makes 9 different tiles possible, the 9 tiles in the *Subulata*.
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43. Board Game: TRIFUSION [Average Rating:7.83 Unranked]
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Re-implement of *Mondriaan 2020*. For 2-4 players instead of 2 players. Now with the blue-blue-blue-blue tile too. 2 sets of the 24 possible tiles, so 48 tiles in this *Trifusion*.
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44. Board Game: Digit [Average Rating:5.47 Overall Rank:14101]
Brian Dysart
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San Jose
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The deck of 55 cards shows every way to arrange five sticks contiguously on a grid (reflections included, rotations not). Each player has a hand of cards, and on their turn they try to match one of them by moving a single stick in the existing arrangement.
 
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45. Board Game: SEVEN [Average Rating:7.44 Unranked] [Average Rating:7.44 Unranked]
Néstor Romeral Andrés
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SEVEN is a tile-stacking game that uses polyhexes of 4 hexagons, called tetrahexes. There are 7 different tetrahexes (hence the name of the game).
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46. Board Game: Pent-Up [Average Rating:7.76 Overall Rank:7680]
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Pent-Up uses 12 pentominoes per player (black and 'ice').

A pentomino is a piece composed of five congruent squares, connected along their edges. There are 12 different pentominoes. Pentominoes are well known in the board game community and lots of games use them.
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47. Board Game: The Mystique Deck [Average Rating:7.43 Unranked]
Néstor Romeral Andrés
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The Mystique Deck is a special deck of 60 cards, with each card depicting three different features (instead of two, like a regular poker deck):

Colour: Yellow, red, and blue — the 3 primary colours of pigment. There are 20 cards of each colour.

Suit: Suns, Moons, Arms, and Crowns. Suns and moons are the ‘heaven’ cards. Arms and Crowns are the ‘earth’ cards. There are 15 cards of each suit.

Number: from 1 to 5. Fives are depicted with an open palm, with the corresponding coloured suit in its palm. There are 12 cards of each number.

Moreover, each card has a unique number at the top, from 1 to 60. This is the ‘card number’.

Some examples of cards are:

Three of red crowns,
One of blue suns (also called ace of blue suns),
Five of yellow arms (also called palm of yellow arms)
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48. Board Game: Myrmidons [Average Rating:7.00 Unranked]
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The pieces of Myrmidons plus its expansion have all the combinations of (movement,attack,defense) that add up to nine and have no zeros.
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49. Board Game: 16! [Average Rating:6.00 Unranked]
Chad Smith
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These little dots go around the outside.
Around the outside.
Around the outside...

(Sorry, too much Eminem as a youth...)
 
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50. Board Game: Tomoe [Average Rating:5.25 Unranked]
Markus Hagenauer jr.
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Surheim
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- triple hexagon tiles with black and white areas
- each area connects no more than two corners (does not branch out)

So there are 4 possible tiles:

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