[Narrator] The answer is 19.
Some of this we need to compute the key space.
Well, the key is just a permutation of the alphabet.
We have 26 choices for what A could map to.
We have 25 choices for what B could map to.
We have 24 choices for what C could map to and so on through the alphabet.
This is equal to 26 factorial, which I won't attempt to write out but will show you in python.
Let's define a factorial function, and we get this rather large number.
What we need to know now is how this compares to the message space.
The number of possible messages of length N,
while each letter in the message can be any letter in the alphabet.
That's just 26 to the N.
We're going to find the first number N, where 26 to the N exceeds factorial 26,
and we get 19, and we can confirm that.
That 26 to the N is indeed greater than factorial of 26;
26 to the 18 is less than it though.
