# The Security to the Party [Part 17!]

You arrive at the party and the host personally comes out to greet you. He invites you in to the party and takes you to his office.

He gives you a numbered list of ingredients for his famous meatball recepie, and tells you that some of the ingredients are red herrings (but none of them are red herring). He has encoded the numbers of the correct ingredients; you have to figure out how to decode them into the proper numbers. He gives you some examples: "6" decoded is "20", "2" decoded is "4", and "3" decoded is "8".

Your friend has given up. He says good bye and leaves. The host tells you that the correct ingredients are those with numbers decoded from "1", "7", "10", and "9". What ingredient numbers are correct?

By the way, if you get this wrong a trampling elephant is waiting!

• He's saying there's a numbered list of various ingredients; some of them are "correct" in some way, but others are not. The "correct" ones are the ones whose numbers are the "answers" to 1, 7, 10, and 9. – TheRubberDuck Nov 11 '14 at 20:14
• @Envision You should be a mod y'know. – warspyking Nov 11 '14 at 20:50
• @warspyking I just don't have anything better to do! – TheRubberDuck Nov 11 '14 at 20:52
• @Envision Exactly! – warspyking Nov 11 '14 at 21:03

One would think:

$4x-4$

Which gives

"0", "24", "36", "32"

Edit

Jumping prime numbers. Start from $x$ jump $x$ primes (including $x$) and add one.

Resulting in

2, 30, 42, 38

• None of these are correct. By now you should know party-security questions are never obvious. – warspyking Nov 11 '14 at 20:56
• Wait! Where is that elephant-umbrella I had? – JNF Nov 12 '14 at 7:32
• Then again, I do need some additional clue besides not being obvious, since it does fit... – JNF Nov 12 '14 at 7:37

The sequence is

powers of 2 in hexadecimal, 2^6 = 32 = 0x20 2^2 = 4 = 0x04 2^3 = 8 = 0x08

So

2^1 = 2 = 0x2 2^7 = 129 = 0x80 2^10 = 1024 = 0x400 2^9 = 512 = 0x200

Therewithal

2,80,400,200

• $2^6 = 64$ is what they've taught me... – JNF Nov 11 '14 at 20:32
• @JNF Base 32 then ;) – Martin Ender Nov 11 '14 at 20:32
• Nope #1 was correct though. – warspyking Nov 11 '14 at 20:53