# The security to [party 40]

The 40th party of the new year is being held at a local mansion. The host is very rich and his success is because of one thing — his famous recipe for Linguini! So rich indeed, that 39 parties have already occurred in a span of 13 days.

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.

For $$1 \le n \le 9:$$

The $$n$$th guest arrives, whereupon the guard, holding a mirror, says $$n,$$ the guest says $$f(n),$$ and the guest is let in. Note: the 9th guest happens to be your friend.

Your hearing allows you to pick up that $$3, 6, 8, 7, 10, 10, 8, 9, 4$$ are $$f(1), \dots, f(9)$$ respectively.

It's getting late, about 7 or 8. So you pull up to the guard and he's holding a pair of dice. If anything, you could say this mansion is rare. But you don't say anything yet, for the guard has not given you your number yet.

Now the guard says "10". How do you respond, given that the only viable option is to utter another natural number?

• And here I was taking the Fresh Prince hint. James Avery (Phil Banks) was in a film called "The Linguini Incident" I figured my friend would be Jazz, and thought the 4 that he said could be related to the letters in his name. So Viv would be 3, and then it all fell apart. Then I started looking at episodes starting with Ep. 40. Wasted hours! Commented Jan 15, 2019 at 2:56

You should say

3

Because

$$f(n)$$ is the Scrabble value of the number $$n$$ when written in English

Example

$$f(8)$$ is the Scrabble score of EIGHT which is $$1+1+2+4+1 = 9$$

• $$\,$$Correct. Commented Jan 14, 2019 at 23:10