Resolving the Middle Pair

Two survivors disagree about one thing

You have judged the extremes and struck the orderings that contradict them, and two choices are left. Look at what they have in common: they open with the same label and they close with the same label. The only place they part company is the two middle slots, and there the same two labels appear in opposite order.

The item has collapsed into a single question: of these two specific angles, which one is smaller? Not a ranking, not four panels — one comparison, and the answer to it picks your choice.

Rank the four angles from SMALL to LARGE.

A

3 - 1 - 4 - 2

B

3 - 2 - 4 - 1

C

4 - 2 - 3 - 1

D

3 - 4 - 2 - 1

The extremes here are panel 3 at one end and panel 1 at the other. That kills choice A, which ends with 2, and choice C, which opens with 4. Choices B and D both open with 3 and end with 1 — and between them, B claims panel 2 comes before panel 4 while D claims the reverse. Everything now rides on panel 2 against panel 4.

Isolate the two

Stop looking at the other two panels. They have done their work, they cannot change the answer, and leaving them in view invites you to re-litigate a decision you already banked.

Those are the two candidates lifted out of the item, drawn exactly as it drew them. With only two openings in front of you the comparison is as clean as this section ever gets: pick a ray from each, turn them onto a common heading in your head, and read which of the remaining rays swings further round.

Why it is right to leave this until last

The two extremes were separated by every gap in the set added together. These two are separated by one gap — 9° to 16° apart in an easy item, 4° to 8° in a medium one, 2° or 3° in a hard one. That is as narrow as anything the item contains, and a small fraction of the span that made the extremes judgment so comfortable.

So this is the hardest comparison you are still required to make, and the sequencing is deliberate. Doing it first would mean spending your freshest attention on the least reliable reading in the item and then carrying whatever doubt it produced into everything else. Doing it last means every other judgment is already banked and cannot be disturbed by how this one goes.

Even a coin flip pays

Suppose you genuinely cannot separate the two. You are choosing between two orderings rather than four, so a guess lands at one in two instead of one in four. The extremes work has already doubled your odds, and it did so using the only comparison in the item you could make confidently.

That is worth remembering under time pressure. There is no version of this method where the early effort is wasted — the worst case is a fifty-fifty on an item you would otherwise have guessed blind, and the best case is that the extremes finished it without this step at all.

Check by re-deriving, once

When you have made the call, confirm it the cheap way: read your chosen ordering off against the panels once, front to back, and see that it describes what you see. Ascending order, smallest label first.

Do not go back and re-audit all four choices. Two of them were killed by an extremes verdict you had good reason to trust, and re-opening that verdict on the strength of a shaky middle comparison is how a correct answer turns into a wrong one. One forward pass, then commit.

A

3 - 1 - 4 - 2

B ✓

3 - 2 - 4 - 1

C

4 - 2 - 3 - 1

D

3 - 4 - 2 - 1

In degrees: #3 = 42°, #2 = 47°, #4 = 52°, #1 = 58°. Ray length is a distraction — compare the openings near each vertex.

Panel 2 is the smaller of the pair, so B is the answer. When you practice, the generator reports the true degrees after you answer — which makes this the one step in the method you can actually calibrate. Track how often your middle call is right and you will learn the separation at which your own eye stops working.

The four angles from that item, redrawn in rank order on a common heading. The extremes stand 16° apart and the middle pair 5° — the whole reason one of those comparisons was free and the other was not.

The takeaway

When two orderings survive the extremes check, they differ only in which of the two middle-ranked angles comes first, so the item reduces to one binary comparison. Isolate those two panels, ignore the rest, and compare them only against each other. They are separated by a single gap, which makes this the narrowest judgment you are still obliged to make and the right one to save for last. Confirm by reading your ordering forward once — and if the call will not come, a fifty-fifty here is already twice what the item was worth before you started.