[FORUM DOLLARS] Math questions!

[K73SK]

So, I was having fun in the chat with trying to confuse Lonewulf with some number patterns that I told him to find the math equations I came up with for. So with this thread, I'm offering my forum dollars for answers to random math questions I come up with. If there's no answer within 1 (maybe 2) weeks, I'll provide the answer with a new question to answer. Note that these aren't supposed to be extremely simple elementary math questions. They're supposed to be more for those of us who enjoy complicated math and like to put our brain to the test. With the question, I'll show the amount of my own forum dollars I'll give for the answer.

Edit:
Please explain how you got your answer as well. This will not only help others understand the resulting answer, but also prove you're not just using some online resource to get your answers.

So let's begin!

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Question #1 - 100G
What's the sequence to these numbers? Note that there are an infinite number of solutions, so your answer may not match mine. Provide the sequence as an equation with 'x' as your variable. The sequence starts with x = 1. I'll provide the numbers up to where x = 10.

-2, 29, 112, 271, 530, 913, 1444, 2147, 3046, 4165

Answer: Here

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Question #2 - 25G
Decrypt the following message:
41 2D 48 2D 27 62 C 6 79 C 41 2D 48 F 6B F C 6B 15 C 15 6 C 1A 6 6 6F 4D

Answer (sort of): Here

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Question #3 - 20G
Question: 251 tickets are given to 251 different people in an audience. There are five different prizes to be given to some lucky winners of the right numbers. How many ways can the prizes be awarded to the people in the audience if the people holding ticket number 241, 200, and 39 all win prizes, but the people holding ticket numbers 112 and 84 do not win any prizes?

Answer: Here

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Question #4 - 5G per problem
Number -> Base-40 representation
0-9 -> 0-9
10-35 -> A-Z
36, 37, 38, 39 -> !, $, ^, &

Convert these TO base-40 FROM base-10:
1.) 42 (Answered Here)
2.) 115 (Answered Here)
3.) 283572 (Answered Here)
4.) 293859235236333 (Answered Here)

Convert these FROM base-40 TO base-10:
5.) $K (Answered Here)
6.) IEA!932 (Answered Here)
7.) AO&J42WA^!K (Answered Here)
8.) ILOV3L3GAIA!! (Answered Here)

[Nightshade]

4x^3 + (x+1)(2x-5)

Or:

4x^3 + 2x^2 - 3x - 5

[K73SK]

I've added the following edit:
Please explain how you got your answer as well. This will not only help others understand the resulting answer, but also prove you're not just using some online resource to get your answers.

Question #2 - 25G (only cheaper because I'll go poor fast if they're all 100G lol)
Decrypt the following message:
41 2D 48 2D 27 62 C 6 79 C 41 2D 48 F 6B F C 6B 15 C 15 6 C 1A 6 6 6F 4D

[GoldenPower89]

Decrypt the following message:
41 2D 48 2D 27 62 C 6 79 C 41 2D 48 F 6B F C 6B 15 C 15 6 C 1A 6 6 6F 4D

Uh... can you give us a hint?

[K73SK]

07/19/2014 if no one solves it before then, yes. I'll post the solution on 07/27/2014 if no one has solved it.

[Redhollowlives999]

That's a little far off; especially for just 25G.

[Nightshade]

Here's something to work with:

Code: Select all

HEX(?)  41 2D 48 2D 27 62 C  6 79  C  41 2D 48 F  6B  F  C  6B  15 C  15 6 C  1A 6 6 6F  4D
DEC     65 45 72 45 39 80 12 6 121 12 65 45 72 15 107 15 12 107 21 12 21 6 12 26 6 6 111 77
MOD 26  13 19 20 19 13 02 12 6 17  12 13 19 20 15 03  15 12 03  21 12 21 6 12 26 6 6 07  25
A-# Eq   M  S  T  S  M  B  L  F Q   L  M  S  T  O  C   O  L  C   U  L  U  F L  Z F F  G  Y

Now, there's obviously another layer of encryption beyond this, but if someone wants to use this as a first step, feel free to do so. I won't have time to work on this until Thursday at the earliest.

[K73SK]

That's a little far off; especially for just 25G.

Yup. It's for fun, after all.

[K73SK]

I came to realize you MIGHT need the "key" in order to decrypt the message, but I'm not sure. Just in case, here's a hint now to see if you're able to get it without so.

Only consider the first 128 characters of the ASCII table.

[K73SK]

Because I now realize that the function isn't one-to-one, it's very likely that the answer won't be solved without the key.

The key: (x^2 + 4)mod127

You may be able to encode it, but I'm looking for someone to show me the work on decoding it, not encoding it.