The Two Things A Board Can Change
Add a filter, or add a choice to one that exists. The only two moves, and one multiplies the resolution while the other barely moves it.
Reference
One more facet
One more facet, one more value
The two edits a board can make, priced.
×k against ×(k+1)/k
9 notes in this part
Adding A Filter
A new facet of size k multiplies the cells by k and the questions by k plus one. The largest edit, and the only one that changes the subject.
Reference
Adding A Choice
One more option inside a filter multiplies the cells by k plus one over k. The cheap edit, and nearly always the one that gets done.
Reference
The Edits Commute, Exactly
Every edit multiplies by a fixed factor, so a sequence can be reasoned about one at a time and in any order. That is not true everywhere.
Analysis
Taking A Filter Away
Removing a filter divides the resolution by its size. It is the only edit that makes separable listings inseparable, and readers cannot see it.
Reference
Splitting One Filter Into Two
Replacing a facet of six with facets of two and three leaves the resolution alone and multiplies the questions by twelve sevenths.
Analysis
The Edits Ranked By What They Buy
Five edits, priced against one board. The largest multiplies the resolution by six; the smallest multiplies it by one and changes the questions anyway.
Reference
When A Board Runs Out Of Moves
A board runs out of moves at six facets of six. Past the bounds the method still works and the statements about collisions do not.
Analysis
What No Edit Can Buy
Three things no edit reaches: a distinction with no filter, a result size off the ladder, and a reader's knowledge of what is missing.
Analysis