In the 50th anniversary special, when Clara told him to be a Doctor, he thinks up a plan:
DOCTOR: Gentlemen, I have had four hundred years to think about this. I've changed my mind.
WARRIOR: There's still a billion billion Daleks up there, attacking.
DOCTOR: Yeah, there is. There is.
DOCTOR 10: But there's something those billion billion Daleks don't know.
DOCTOR: Because if they did, they'd probably send for reinforcements.
CLARA: What? What don't they know?
Then they realize something in their minds that surprises them:
DOCTOR: This time, there's three of us.
WARRIOR: Oh! Oh, yes, that is good. That is brilliant!
DOCTOR 10: Oh, oh, oh, I'm getting that too! That is brilliant!
DOCTOR: Ha, ha, ha! I've been thinking about it for centuries.
WARRIOR: She didn't just show me any old future, she showed me exactly the future I needed to see.
MOMENT: Now you're getting it.
DOCTOR: Eh? Who did?
WARRIOR: Oh, Bad Wolf girl, I could kiss you.
MOMENT: Yeah, that's going to happen.
DOCTOR 10: Sorry, did you just say Bad Wolf?
CLARA: So what are we doing? What's the plan?
WARRIOR: The Dalek fleets are surrounding Gallifrey, firing on it constantly.
DOCTOR 10: The Sky Trench is holding, but what if the whole planet just disappeared?
CLARA: Tiny bit of an ask.
DOCTOR 10: The Daleks would be firing on each other. They'd destroy themselves in their own crossfire.
WARRIOR: Gallifrey would be gone, the Daleks would be destroyed, and it would look to the rest of the universe as if they'd annihilated each other.
CLARA: But where would Gallifrey be?
DOCTOR 10: Frozen. Frozen in an instant of time, safe and hidden away.
WARRIOR: Like a painting.
Then on Gallifrey the 3 Doctors tell the Council the plan:
DOCTOR: We're flying our three Tardises into your lower atmosphere.
DOCTOR 10: We're positioned at equidistant intervals around the globe. Equidistant. So grown up
WARRIOR: We're just about ready to do it.
GENERAL [OC]: Ready to do what?
DOCTOR: We're going to freeze Gallifrey
GENERAL: I'm sorry, what?
DOCTOR 10: Using our Tardises, we're going to freeze Gallifrey in a single moment in time.
WARRIOR [on monitor]: You know, like those stasis cubes? A single moment in time, held in a parallel pocket universe.
DOCTOR: Except we're going to do it to a whole planet.
DOCTOR 10: And all the people on it.
GENERAL: What? Even if that were possible
GENERAL [OC]: Which it isn't, why would you do such a thing?
DOCTOR: Because the alternative is burning.
DOCTOR 10: And I've seen that.
DOCTOR: And I never want to see it again.
GENERAL: We'd be lost in another universe, frozen in a single moment. We'd have nothing.
DOCTOR: You would have hope. And right now, that is exactly what you don't have
GENERAL: It's delusional. The calculations alone would take hundreds of years.
DOCTOR: Oh, hundreds and hundreds.
DOCTOR 10: But don't worry, I started a very long time ago.
Then other TARDISes come into the sky, which turn out to be the Doctor's past incarnations:
DOCTOR 1: Calling the War Council of Gallifrey. This is the Doctor.
DOCTOR: You might say I've been doing this all my lives.
DOCTOR 2 [on monitor]: Good luck.
DOCTOR 3 [on monitor]: Standing by.
DOCTOR 4 [on monitor]: Ready.
DOCTOR 8 [on monitor]: Commencing calculations.
DOCTOR 5 [on monitor]: Soon be there.
DOCTOR 7 [on monitor]: Across the boundaries that divide one universe from another.
DOCTOR 6 [on monitor]: Just got to lock on to his coordinates.
DOCTOR 9: And for my next trick.
GENERAL: I didn't know when I was well off. All twelve of them!
ANDROGAR: No, sir. All thirteen!
(the 12th Doctor Peter Capaldi comes in)
ANDROGAR: Sir! The Daleks know that something is happening. They're increasing their fire power.
GENERAL: Do it, Doctor. Just do it
GENERAL [OC]: Just do it.
I'm confused: what comes in their mind when 11 says "this time there's 3 of us"? What calculation did he start a very long time ago? Why was the Doctor's best strategy for saving Gallifrey to get help from his 13 incarnations?