What comes first

The opening position, counted.

c times P(n−1, r−1)

8 notes in this part

Of all the orders a reader might meet a set in, those opening with something verifiable number c times the arrangements of everything after.

Definition

The share of arrangements opening with something checkable is the checkable count over the published count. Every factorial cancels out.

Recount

A reader who meets one statement collapses the record to one question: was it checkable? Sixty-three shapes are of that kind.

Analysis

Three shapes on one page where a fifth of arrangements open verifiably and the blind share runs from three fifths down to two fifteenths.

Recount

Blind encounters can be ruled out with half a set verified. Guaranteeing a verifiable opening takes all of it, and the asymmetry has one cause.

Analysis

The share of arrangements whose second statement is checkable equals the share for the first. The opening is special in effect, not in frequency.

Reference

With one checkable statement in seven, an encounter opens with it one time in seven at any depth, while the blind share falls fivefold.

Recount

The opening count is the figure here most exposed to its convention, because a reader's entry point is the least random thing about them.

Caution