What Kind of Math is Water Sort Puzzle?

[Anonymous]

Question for mathematicians:

There’s this online app for a game called water sword puzzle. There are test tubes filled with different colors of water, and you can only place red water on top of other red water or into an empty test tube. As it gets more complicated, It’s harder and harder to solve the puzzle. I’m positive there’s a type of math people study that address this type of problem. I’m wondering what it’s called? What branch of mathematics is this?

[Anonymous]

Here’s an example of the puzzle:

https://m.youtube.com/watch?v=3hE-bNHgUn4

[Anonymous]

Honestly, it looks closest to topology to me. That’s the study of how things are shaped and extends to interconnections and networks. If you imagine the test tubes colors and different strings that must be unknotted that lay accross other strings, it turns into a topology problem.

[Anonymous]

It looks a bit like a constraint satisfaction problem. Specifically, a "job shop" optimization problem. You have a set of operations you can perform to reach a final state (that is easily tested.) The goal is to find the a way to get there, if possible, and for computer scientists, the minimum number of operations. It's NP hard.

https://en.wikipedia.org/wiki/Job_shop_scheduling

[Anonymous]

Anonymous wrote:Honestly, it looks closest to topology to me. That’s the study of how things are shaped and extends to interconnections and networks. If you imagine the test tubes colors and different strings that must be unknotted that lay accross other strings, it turns into a topology problem.

It feels like a topology problem to me, but I never studied it so I wasn't sure.

But solving the puzzles reminds me of solving knot problems.

[Anonymous]

graph theory, although it's been so long I couldn't begin formulate the type of problem. And yes, it can involve optimization depending on how many variables (test tubes and colored layers) you have. If you constrained it to a very simple version (not level 603!) you would be able to test all the choices you have.

but really graph theory and topology lead into each other

[Anonymous]

Combinatorics/discrete mathematics sorting problem. You basically consider the colors as labels that have to be sorted.

[Anonymous]

Anonymous wrote:Combinatorics/discrete mathematics sorting problem. You basically consider the colors as labels that have to be sorted.

It's not quite sorting because you aren't free to randomly insert colors wherever you like. It's similar to the Towers of Hanoi.

[Anonymous]

Anonymous wrote:Combinatorics/discrete mathematics sorting problem. You basically consider the colors as labels that have to be sorted.

that too, but then combinatorics comes with graph theory!