On: Here's a puzzle game. I call it Reverse the List of Integers

[Someone]

> If you wanted to support a game up to the integer 10 you would need 10 posts with lengths from 1 to 10 units, and 10 post holes.

You’d also need a way to represent the order of the posts (the game is about a list of integers, not a set, so you can’t move from [4,5,6] to [10,5], for example)

I think a halfway decent visualization is one where you have n different cylinders of lengths 1 through n and a gutter of length of the sum of the numbers you start with (in the [4,5,6] example that would be 15). Next, place the cylinders for the starting position in the gutter in the order given, so that it completely fills it. Keep the others elsewhere.

Allowed moves then are:

- replace two cylinders that are side by side in the gutter by one of the sum of their lengths that you have available.

- replace a cylinder in the gutter by two available cylinders that together have the same length.

I think this way to visualize the game also might lead to a physical construction, but I don’t see on yet.

[dwallin → Someone]

I really like this. I could see constructing a physical artifact for a specific case of this game.

According to another comment, the best puzzle with a high number of 6 is [1,6,3] with a minimum of 14 moves.

This would mean you have 6 total rods, and two gutters. The puzzle gutter with a length of 10, and the storage gutter with a length of 11.

If you want more visual symmetry a high number of 7 allows you potentially 2 gutters of length 14.

[Someone → dwallin]

Thinking it through a bit more, I would consider a variation on this game, where you don’t have a list but a ring buffer.

Then, you can replace the linear gutter by a circular one and replace the cylinders by parts of a torus. That would make for a cooler look of the game (on the other hand: how would you easily see you’ve completed the puzzle?)

Unfortunately, you won’t be able to put the ‘spare’ parts in a concentric circle as that would have a different radius.