72

The number 72 plays a significant role in Assassin's Creed: Brotherhood. It is the password, which needs to be spoken, in order to the gain access to the Colosseum Vault. Also, when Lucy's team of Assassins enter the Vault, there are 72 days remaining until Abstergo launch their satellite mounted with a Piece of Eden.

Creation and Clues
Ezio discovered, or created the password in 1500's and used it to seal the Apple of Eden within the Colosseum Vault. Leonardo Da Vinci, a long-time friend of Ezio's, persuaded him to leave a clue to the password behind. Desmond knew that Ezio had returned to the Villa Auditore due to a vision he had from the Bleeding Effect. Presumably Ezio left the password in such a way that it could only be seen in Eagle Vision, either for a fellow Assassin or descendant to find it.

In Mario's study, a bookcase conceals the entrance to a secret passageway leading down some stairs to the Sanctuary. At the top of the stairs, engraved into the wall, is an equilateral triangle. The triangle is split into nine smaller equilateral triangles. Noticing the marking on the wall, Shaun Hastings mentions this to his fellow Assassins. Desmond then uses his Eagle Vision to reveal three numbers; 1419, 1420 and 1421.

Realization
After discovering the location of the Apple through the use of the Animus 2.0, the Assassins ponder how to access the Vault.
 * Rebecca: It seems to open with a verbally triggered mechanism. I've never seen anything like it.
 * Lucy: You mean it needs a password?
 * Shaun: Try humming Beethoven's Fifth.

The power cuts off disabling the Animus so the team can no longer search Ezio's memories for the password. Desmond goes back to the markings at the top the stairway and calls the others. They discuss the symbol and the relevance of the numbers. The triangular symbol on the wall of the Villa Auditore matches the symbol on the door to the Vault.

Shaun discovers the password and explains to the rest of the team:

"The Tetragrammaton. The 72 name of God. You see? They're all contained within three verses. Exodus 19 through 21. And, get this, you'll like this, if you arrange the four Hebrew letters in God's name within an equilateral triangle; their numerical values add up to the same number: 72"

- Shaun Hastings explains the password to the Modern Day Assassins

They make their way to Colosseum and Desmond, saying '72' aloud, opens the sealed door gaining them access to the Vault and to the Apple.

Trivia

 * It is possible that Ezio asked the Apple for the password and where to leave it. This would explain how he could be sure that Desmond would find it years later.