The Product That Fixes Everything
Multiply the facet sizes together and you have the number of listings a board can tell apart. Everything else about the board can change; that figure cannot.
Reference
Telling apart
What a board can tell apart
The product of the facet sizes, and what it forecloses.
2 to 46 656
8 notes in this part
Two Listings In One Cell
Two listings that agree on every filter become one listing to every question the board permits. The difference is invisible by construction.
Analysis
The Ceiling Is Set Before Anything Arrives
The filters are chosen once; the listings arrive afterwards, for years. Everything countable about a board was fixed in that first decision.
Analysis
What One Number Leaves Open
Three hundred and eighty-one schemas of four hundred and sixty-one share their cell count with another. Four boards in five, unidentified.
Reference
Seven Boards, One Resolution
Seven schemas all tell one hundred and forty-four listings apart, from three filters to six, with questions from 245 to 1296.
Reference
Four Hundred And Sixty-One Schemas
How many structures fit inside the bounds, how they spread across one to six facets, and why the order of filters is not part of a schema.
Reference
Two Cells, And Forty-Six Thousand
The narrowest schema resolves two listings, the widest forty-six thousand six hundred and fifty-six. Both are ordinary boards.
Reference
Why A Facet Starts At Two
A filter with one choice multiplies the resolution by one and the question count by two. It cannot narrow anything, and it still occupies a reader's attention.
Analysis