Agreed, and I also feel no ill will towards the writers. Problem setting is probably a very different skill from writing tutorials that are clear to people who are right on the boundary of understanding the problems. I usually find more enlightenment in the comments after the contest.

During today's contest, I was able to figure out the 2 "trivial" conditions that obstruct a coloring. And after reading the above formula for $$$pos_i$$$, it wasn't hard to prove:

1. The $$$m$$$-th coloring covers the $$$n$$$-th square,
2. Every color is represented: $$$pos_i<pos_{i+1}$$$, and
3. There are no gaps: $$$pos_{i+1} \leq pos_i + len[i]$$$

But this feels quite backward as I still don't know how to come up with the construction in the first place.

I Totally agree with you! If I write tutorial in Chinese, I will write almost detail in the tutorial. But limit to my English writing ability, It's so hard to describe what I think... For example, Just each problem of Div. 2 A, B takes me over two hours to complete it. But I will try to add something in the weekend.

Now I have added more discussion about this problem, Including some overall strategy to solve construction problems. Feel free to read it : )