Understanding “The Three Scarfwearers” (for anyone out there who feels like a concussed bee). I've referred to Scarfwearer as he travels in time, by re-labelling him whenever the TARDIS materializes.

Scene 1

As we begin Scarfwearer is looking for his cup. He spots his cup on the chair and sits down.

The gate slams, so he goes to see if there’s someone there.

His scarf pulls the cup off the chair and it smashes.

He goes back to sit down, picks up the pieces and realizes that he could go back in time in the TARDIS to get the cup.

He gets up again, leaves through the side gate and enters the TARDIS.

Scene 2

He rematerializes (as Scarfwearer2) in the past but in the same location, leaving his hat behind in TARDIS.

He returns to the gate, and discovers that Scarfwearer1 is already there. He didn’t go back far enough.

He slams the gate, hears the cup break and hides at the side.

Scarfwearer1 comes through the door, but doesn’t see Scarfwearer2.

At this point, we already have the classic temporal paradox going on here – the original gate slam that led to the cup being broken was Scarfwearer2 arriving. If the cup hadn’t broken Scarfwearer1 wouldn’t have gone back in time as Scarfwearer2 to retrieve it.

Scarfwearer2 returns to the TARDIS for another attempt.

Scene 3

Scarfwearer3 rematerializes further in the past, and hitches up his scarf, to be less conspicuous and avoid accidents.

This also helps us distinguish him from Scarfwearer2…

He comes through the gate and finds the chair empty. He takes the cup from it and leaves with it.

At this point, history and the order of events has been changed, and we need a new diagram.

Meanwhile, unseen, Scarfwearer2 has arrived and left, as described later.

Scarfwearer1 appears, looks puzzled and starts searching for his cup.

Scene 4

On his way back to the TARDIS Scarfwearer3 sees Scarfwearer2 enter the TARDIS and take off in it. He doesn’t manage to get in before it leaves, and finds that his TARDIS interior is now in the original reality (original diagram).

There’s a certain amount of dramatic licence here, but I think it’s consistent with Father’s Day. Sort of.

He’s now stuck with a police box with an empty interior, while Scarfwearer1 searches for his cup. Eventually he realizes that if he can get Scarfwearer1 into the TARDIS he can hitch a ride.

Scene 5

Scarfwearer3 picks up the cup and creeps back to Scarfwearer1 (who’s dozing in the chair at this point).

He puts the cup where it’s sure to get broken and creeps round to the gate.

He slams the gate.

Scarfwearer1 gets up to investigate, breaks the cup and then decides to go back in time.

Scarfwearer1 enters the TARDIS, closely followed by Scarfwearer3 and travels back in time.

There’s a certain amount of dramatic licence here, but the idea is that breaking the cup restores the time-stream enough that the TARDIS interior reconnects with the time stream that Scarfwearer3 is in.

Scene 6

Scarfwearer2 leaves the TARDIS, wearing his hat (which is a continuity error) and moves the ladder (which is an in-joke)..

Scarfwearer3 pokes his head out

During this Scarfwearer2 encounters Scarfwearer4 (yes there are actually four!), as we’ll see later.

Scarfwearer2 returns and takes the TARDIS further back in time in order to retrieve the cup again.

Scene 7

Scarfwearer4 pokes his head out for the first time

Scarfwearer3 leaves the TARDIS.

Scarfwearer4 then leaves the TARDIS, with his hat.

He returns to his chair after Scarfwearer3 has taken the cup and dozes off.

The Gate slams…

So when the gate slams at the end, Scarfwearer4 is about to get a visit from Scarwearer2, who’s just arriving to look for his cup, only this time there’s no cup to break...

But the story doesn’t really end there: