Super fair. I did not read that section in detail, and missed your interpretation on my skim. I interpreted it to mean “in the planning literature, we typically see k=3 for n<6” (which we do!), noted that they did not say the alternative value, and then went with the k=3 value they did say in the main body.
You’re right that your interpretation is more natural. If they actually used k=4, then the problem is solvable and the paper was (a bit) better than I portrayed it to be here.
Worth noting that, even assuming your interpretation is correct, it’s possible is that the person who wrote the problem spec did know about the impossibility result, but the person running the experiments did not (and thus the experiments were ran with k=3). But it does make it more likely that k=4 was used for n>5.
I think my statement above that “they did not say” “a different value of k (such that the problem is possible)” still seems true. And if they used k=4 because they knew that k=3 is impossible, it seems quite sloppy to say that they used k=3 in the main body. But a poorly written paper is a different and lesser problem to the experiment being wrong.
Super fair. I did not read that section in detail, and missed your interpretation on my skim. I interpreted it to mean “in the planning literature, we typically see k=3 for n<6” (which we do!), noted that they did not say the alternative value, and then went with the k=3 value they did say in the main body.
You’re right that your interpretation is more natural. If they actually used k=4, then the problem is solvable and the paper was (a bit) better than I portrayed it to be here.
Worth noting that, even assuming your interpretation is correct, it’s possible is that the person who wrote the problem spec did know about the impossibility result, but the person running the experiments did not (and thus the experiments were ran with k=3). But it does make it more likely that k=4 was used for n>5.
I think my statement above that “they did not say” “a different value of k (such that the problem is possible)” still seems true. And if they used k=4 because they knew that k=3 is impossible, it seems quite sloppy to say that they used k=3 in the main body. But a poorly written paper is a different and lesser problem to the experiment being wrong.