The Security to the Party [Part 6]

Question

A party is being held at a local mansion. The host is very rich and his success is because of one thing — his famous recipe for Spaghetti!

The only guests that may attend are people who correctly reply to the guard at the door.

Here's where you come in. You and a friend are trying to steal this recipe. You sneak by and listen to the passwords.

The first guest arrives. The security says "1", and the guest replies "0".

The second guest arrives. The security says "6", the guest replies "0".

The third guest arrives. The security says "7", the guest replies "0".

Your friend thinks he's got it all figured out so he walks up to the door and the security says "2". He replied "0", and is tarred and feathered and sent away in shame.

Another guest arrives, security says "9" and he says "3" to get in.

Hint:

Another guest arrives, security says "2" and he says "2" to get in.

Hint #2:

Another guest arrives, security says "4" and he says "3" to get in.

Hint #3:

Another guest arrives, security says "0" and he says "3" to get in.

You walk up and get a "8" from security. What is your response?

Hint #4:

8. You might not think that's a hint, but it is if you think outside the box.

Hint #5 (last hint and I will post the answer later tonight if still unsolved):

See my profile.

Thanks for the ideas, credits to:

Part 1 was created by warspyking and is found here: The Security to the Party

Part 2 in Mew's version The Security to the Party [Part 2]

Part 3 in skv's version The Security to the Party [Part 3]

Part 4 in JNF's version The Security to the Party [Part 4]

Part 5 in user3804649's version The Security to the Party [Part 5]

Answer 1

You walk up and get a "8" from security. What is your response?

The correct response is 4.

The rule is to convert the number into capitalized word form (EIGHT), look at the first letter, and take the minimum number of straight lines needed to form it. Four straight lines are needed to form an uppercase E.

What was Hint #4 referring to?

"8. You might not think that's a hint, but it is if you think outside the box."

That is referring to Part 8 of this series. The answer for that question requires looking at the word form of the number and counting things.

What was Hint #5 referring to?

"See my profile."

On my profile, the most upvoted thing is this answer, which involves counting straight lines.

Answer 2

I would say "2". The formula to calculate the answer seems to be x=Floor(2(1-cos(n)))