## Reverse the list of integers

A game invented by Alexandre Muñiz: https://mathstodon.xyz/@two_star/112242224494626411

Here's a puzzle game. I call it Reverse the List of Integers. How it works is, you start with a list of positive integers, (e.g. [7, 5, 3]) and your goal is to make the same list, in reverse ([3, 5, 7]). You have two moves you can make:

1) Split an integer into two smaller integers. (e.g. [7, 5, 3] → [6, 1, 5, 3]) 2) Combine (add) two integers into a larger one. (e.g. reverse the last e.g.)

There are two restrictions that seem natural for making this into an interesting game:

1) You can never make an integer greater than the largest integer in the original list. 2) You can never make a move that results in the same integer appearing in the list more than once.