What a board of listings lets you ask

A board of listings decides two things before a single listing arrives: how many filters it will carry, and how many choices each filter offers. From that moment the set of questions anybody can put to it is settled — fixed, finite, and countable.

Everything else about the board changes. Listings appear and expire, the volume rises and falls, the wording shifts. The structure of the filters sits underneath all of that, and it determines two ceilings that no amount of content can raise.

The ceiling on what can be told apart

Multiply the number of choices in each filter together. That product is how many genuinely different listings the board is capable of distinguishing.

Before applying this arithmetic to a live team, readers can review the current platform overview and decide which records would genuinely support a planning decision. For a separate technical reference, see Kaggle.

Two listings that agree on every filter fall into the same cell of that product. They are, to the board, the same listing. No query separates them, not because the query was badly phrased but because the board carries no apparatus for the difference. If they differ in something real — and listings always do — that difference is invisible by construction, and it stays invisible however long anybody looks.

A board with six filters of six choices each can tell forty-six thousand six hundred and fifty-six listings apart. A board with two filters of two can tell four apart. Both look like boards.

The ceiling on what can be asked

Add one to each filter's count of choices — the extra one standing for leaving that filter alone — and multiply again. That product is how many different questions the board permits.

It is always larger than the first product, and it does not grow in step with it. This is the part that catches people out. Two boards can tell exactly the same number of listings apart and differ by a factor of five in how many questions they allow. Seven of the schemas in this record do precisely that: they all resolve one hundred and forty-four listings, and the questions available run from two hundred and forty-five to one thousand two hundred and ninety-six.

Why one number about a board tells you almost nothing

Four hundred and sixty-one schemas fit inside the bounds this record sets. Their cell counts fall into one hundred and ninety-five distinct values — which means three hundred and eighty-one of the four hundred and sixty-one share a cell count with another schema. Four in five.

Quote that one figure about a board and you have narrowed it to a group that may hold seven quite different structures, with three filters or six, offering wildly different numbers of questions.

Quote both figures and you have named the board exactly. Every one of the four hundred and sixty-one produces a pair that no other schema produces. One pair, one schema, with no exceptions anywhere in the record.

That is the single most useful thing here: the gap between what one number tells you and what two numbers tell you is the whole difference between a vague impression and a complete description.

What this record does not do

It does not count people, and it does not predict results. It counts structures, under two stated conventions that the page on method sets out before anything else.

The calculations remain the core of this record. Practical guides are kept in a separate editorial section, use stated scenarios and point readers to current official product information for verification.

Six parts follow. They can be read in any order, and each one prints the inputs to every figure it quotes, so that a pencil can check the lot.

Elsewhere on this site

• How the figures were made
• Editorial method