Permutations

Permutations

Years ago I made a prototype for a board game set in a dark-humour dystopia where players took on the role of waste management professionals. Their job, to sort the garbage that accumulated at their central processing facility. During the game, players salvaged and smuggled various materials for themselves, which they could then craft into various items that granted different advantages and abilities.

The salvageable idea from this game is the use of permutations to create an organized crafting system. Because a core mechanic of the game was about crafting dozens of items, I wanted to make sure there was a way to keep track of the materials used for each item, and that each crafting “recipe” was unique.

There are many ways to generate permutations, and many parameters that can be applied along the way, but let’s start with a simple example using numbers: 1, 2, 3.

If we scrambled these numbers into every possible 3-digit arrangement, we’d get six permutations, like so: 123, 213, 312, 132, 231, 321.

Ok, neat, I guess. But how do we use this to craft items?

First, let’s make the numbers a little more tangible by assigning materials to each digit, materials that players can collect and craft into items. How about materials for a wilderness survival game?

Wood

1 = Wood

I'm totally a stone. Not a potato.

2 = Stone

Twine

3 = Twine

1, 2, 3. Wood, stone, twine. What could a player create with this?

Wood + Stone + Twine = Hammer

Ok! So we have the materials to make a hammer (or an axe, if you like). But there’s an issue when applying permutations in this way. No matter how we shuffle it (123, 321, 312, etc.), it results in the same handful of materials. That’s not necessarily useful for generating unique crafting recipes. How can we add more variety and ensure that each permutation is unique? Here’s where it gets good — says me.


Stick with the same numbers (1, 2, 3), but allow for the repetition of numbers within each 3-digit arrangement. For example: 111, 112, 322, etc.

This generates the following list of permutations:
111, 112, 113, 121, 122, 123, 131, 132, 133
211, 212, 213, 221, 222, 223, 231, 232, 233
311, 312, 313, 321, 322, 323, 331, 332, 333

Thematically, this can start to give volume and ratios to the materials. For example: 113 (wood, wood, twine) makes me think of a long branch with a short string. Perhaps this crafting recipe could create a long bow.


Next, to ensure that the materials in our recipes are unique, we need to omit subsequent arrangements that are made up of the same numbers. For example: If you have 123, omit 321, 312, etc. This will thin out the list significantly.

Clean up the list so that only unique arrangements remain:
111, 112, 113, 121, 122, 123, 131, 132, 133
211, 212, 213, 221, 222, 223, 231, 232, 233
311, 312, 313, 321, 322, 323, 331, 332, 333

With that, we end up with the following ten permutations: 
111, 112, 113, 122, 123, 133, 222, 223, 233, 333.

Note: You don’t need to do all of this manually. There are lots of online permutation generators that will do these steps for you. A quick search should net you more than a few with different settings you can play with. Fire up a spread sheet, copy the results into a column, and you’re set.


Now that we have our list of unique permutations, all we need to do is think up ten items that could be crafted using the assigned materials. Some might be more obvious than others. If you’re struggling, think abstractly and consider materials in different forms. A single stone could be a solid rock, or a handful of pebbles. Also, try to establish some consistency in how the volume of materials are applied for each item, it will help players to visualize what they’re working with.

Let’s get to it.

PermutationsMaterialsItems
111undefinedundefinedundefinedBundle of sticks (bonfire)
112undefinedundefinedundefinedSpear
113undefinedundefinedLong bow, snare, fishing pole
122undefinedundefinedundefinedSaw
123undefinedundefinedHammer, axe
133undefinedFishing net
222undefinedundefinedundefinedStone marker
223undefinedundefinedBolas
233undefinedAnchor
333Long rope

Bonus round: Let’s not waste the smaller permutations. What if we applied a 2-digit arrangement to the set of 3 materials? What can we make with those?

PermutationsMaterialsItems
11undefinedundefinedSmall twig bundle (campfire)
12undefinedundefinedArrow
13undefinedTorch
22undefinedundefinedFlint
23undefinedSling
33Short rope

Done. A few recipes ended up with more than one possible item, sometimes it’s easy to get carried away with the possibilities. There were some tough ones, too. Like, 122 (wood, stone, stone), creating a “saw” was a bit of a stretch, but I figured someone could line the wood with rows of rock chips from a couple of stones to make a saw-like tool. It was either that or a caveman barbell.


Now that we have an organized method to generate unique crafting recipes and items, we’ll need to seed the game world with materials. This could be done with a simple table and dice rolls, or blind-pulling tokens from a bag whenever players search an area. Thematically, a nearby forest makes wood plentiful and the hillsides are abundant with stone, but the dried vines used for twine is scarce in these parts. In this case, you’d make twine less probable on your table, or have less twine tokens in your bag.

There are all kinds of ways to apply permutations! Try adding more materials, this will expand your options greatly. Experiment with 2-, 4-, or 5-digit arrangements, or try using arrangements that omit certain numbers. Just recognize that the more permutations you generate, the more items you’ll have to think up.

Let me know what crafting recipes and items you come up with on Twitter. Happy permuting!

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