> You can get to with [4, -1, 3, 1] with one step, but I'm not sure where you can go from there. Well, it's easy to show that you can't go anywhere from there:

> You can get to with [4, -1, 3, 1] with one step, but I'm not sure where you can go from there. Well, it's easy to show that you can't go anywhere from there: 1. You can't combine the 1 with the 3, because you'd have two 4s. 2. You can't combine the -1 with the 4, because you'd have two 3s. 3. You can't (usefully) combine the -1 with the 3, because that just means you never took your previous move of splitting that pair out of the 2. Those are all the possible applications of the combining rule. You can't apply the splitting rule either: 1. Splitting the four into positive integers will cause a duplicate. 2. Splitting a negative number out of the four will violate the rule against numbers larger than 4. 3. Splitting the 3 has the same problems. You can't take out a negative number without leaving a residual of 4 or more, and you can't take out a positive number without leaving a residual of 1. 4. Taking a -1, -2, or -3 out of the 1 will leave a duplicate, and taking a positive value out of the 1 is impossible. 5. You can split the -1 into [-3, 2]. But at that point you need to get rid of the 1 in final position so that you can combine the -3 into the 4, and there isn't a way to do that. Once you've gotten here, your list already contains every legal positive value.