Ugh my bank keeps calling me and making me validate my identity by rattling off the card number and security code, to warn me that hackers have charged my card absurd amounts! It would be nice if they called before the hackers steal my money. That's how I memorised it.

God I had that shit down on my first card around 19. Felt like a wizard.

Standard compliance rules generally allow showing the first six and last four digits on a statement or receipt or whatever. That leaves 6 digits, and since you know it has to match the cksum, 1/100,000 odds on straight guess.

You may be able to knock down two more digits if you know which bank and card type (debit, prepaid, etc) it is. The first 6 digits used to encapsulate that data but there's a transition to 8 now.

The fun is in discrete logic! There is a whole field of mathematics (discrete mathematics) that analyzes the logic of situations that involve binary (true/false) statements, such as the solution to this riddle.

The riddle can be summed up as the following:

Let Y represent a question asked of the knights.
Let A(x) be a boolean function representing the answer of the truth-teller.
Let B(x) be a boolean function representing the answer of the liar.

B(x)≡¬A(x)

An answer can only be determined if the knights do not contradict, otherwise it could not be determined which knight was lying, for instance when Y≡(A(Y)∧B(Y))∨(¬A(Y)∧¬B(Y))≡T.
A trivial question whose answer is logically true would result in the following form:

Y≡(A(Y)∧B(Y))∨(¬A(Y)∧¬B(Y))
A(Y)≡T
B(Y)≡F
Y≡(T∧F)∨(F∧T)≡F∨F≡F
∴Y≡F

Such a question would allow identification of which knight is lying, but would not provide information on which door is true.

Let D represent a set of m doors where there is exactly 1 correct door.

∃!n∈ℕ:D(n)≡T∧n≤m

The player ideally wants to discover which value n is correct so they can choose a door accordingly.
Let R represent the following question: "What are all the doors the other knight could say are correct?".
Let S represent all possible answers to the question "What is the correct door?" for each knight respectively.
Let P be the set representing the value n where D(n)≡T, and Q be the set representing all values n where D(n)≡F,

P⊂D
P={n}
Q⊂D
Q=D-P

Thus the following properties are true:

P∩Q=∅
P∪Q=D

Consider that the answer S would be either t∈P if a knight is telling the truth or t∈Q if a knight is lying.
Thus when answering question R:

A(R)≡B(S)≡t∈Q
B(R)≡¬A(S)≡t∈Q

Since question R asks for all possible answers, both knights would provide an answer equivalent to set Q.

∴ the correct answer is D-Q; the one door that neither knight says.

I'm a little rusty on my discrete mathematics, as I haven't done it in 3+ years, but hopefully my answer is logically sound! Feel free to correct me.