I need people good with math like puzzles

[Nekogami]

I'm kinda confused. It's a Neopets plot thing but regardless of why I need to know. If someone could explain the basics, I might understand what to do next.

See http://www.thedailyneopets.com/return-s ... -part-two/

And an excerpt if you will...

The following key works for messages with ONE modifier.
x+x=v
v+c=v

v+x=c
c+c=c

v+v=x
c+x=x

Okay so what I gleen from this is... The sum of C = modifier = modifier.

v = x but the sum of v =/= v and the sum of x=/=x

And that's all I got before I decided that it wasn't making sense, especially if I plug in numbers.

Since 99% of you are smarter than me, I request some kind of guidance on how to approach this. I'm sure math is the key but numerically this really doesn't make sense to me.

Also, everyone's experience in this plot will be different so I don't and can't expect the answers but if I could figure out that premise, I might be able to do it on my own. You know?

Thanks for your help if anyone so cares to give it.

[Besyanteo]

C=0;

v+c=v
v+c-v=0
c=0

c+x=x
c+x-x=0
c=0


v+v=x
x+x=v
x+v=0

There isn't a solution that uses real numbers. *shrug* fuck around with it at random? Or semi-random.

[Idran1701]

Looking at the puzzle, it doesn't seem to involve math at all. The explanation's not very well written, honestly, or I just don't have enough context from that page to understand what it means.

What I think it means, though, is you start with one symbol. Each modifier on the symbol changes it into a different symbol. So if you have x, and the modifier is x, you get v. Then if the modifier to v is c, you get v, and if the modifier for that is x, you get c. So go through a line of that starting with the key to get the target.

Can you show us a screenshot of the whole screen, not just the messages that are on that page?

[Nekogami]

Just an example of the first one ...




Below is an example of a 1Modifier puzzle.


I could just go through and randomly choose for the one modifiers but I'd rather understand the logic behind it so I can figure out the multi-modifier problems.

I mean...it can't just be randomly generated.

[Animala]

Okay, I'll give this a shot.

MATH BACKGROUND INFORMATION:

A little bit of knowledge of modular arithmetic will make this a lot easier to explain. Think of the way a clock works. You have 24 hours in a day, but we count from 1-12 instead. 13 hours is 1 o'clock again. So if you have a number larger than 12, you subtract 12 until you get a number smaller than 12.

Modular arithmetic works similarly, but you can choose any base.

For example, we'll start with the modular base 3, which is how the 1 modifier puzzles work.

There are only three numbers that have any meaning in modular base 3. 0, 1, and 2. if you count mod base 3, you would count 0, 1, 2, 0, 1, 2.

To find out what a number is mod base 3, you subtract 3 until you have a number less than 3 (or divide by 3 and find the remainder, it's the same thing)

So:

0+0 = 0
0+1 = 1
0+2 = 2
1+1 = 2
1+2 = 0 (3 divided by 3 has a remainder of 0)
2+2 = 1 (4 divided by 3 has a remainder of 1)

Each of the symbols represents a number mod base 3. When you modify the key, you add, digit by digit, in base 3. No carrying 1s or anything. This means that V modified by C will always be the same as C modified by V because

V+C = C+V.

The first step is to find out what symbol represents 0. To do this, keep plugging in modifiers until you find a symbol that doesn't change the symbol above it at all. In the 1Modifier example you gave, C represents 0. You can tell because of the first digit. C + V = V. So C is zero.

Here's the wacky part. Pick another symbol. Declare it to be 1 (trust me, this works no matter which symbol you pick). Then work out what the other numbers are based on this. The simplest way to do this is to pick a symbol you have in both the key and the modifiers, so that you can do 1+1 to find out what 2 is. (although this is really easy for 1Modifier problems, since you only have three symbols)

For 2Modifier problems, it's mod base 5. So the numbers are 0, 1, 2, 3, 4.

You follow the same method, using modifiers so that you double up on a symbol in a column. (i.e. V+V+C) If the result is C, then you know V is 0. And you can proceed as before: pick a symbol to be 1, and add 1+0+1 to get the symbol that represents 2.

Once you have the symbols all mapped to numbers, you should be able to predict what the result of any combination of modifiers should be. Unfortunately, you still have to work by process of elimination to find the combination that will give you the answer (or if there's a better method, I haven't found it).

[Nekogami]

I admire your brain.

I'm going to give that a whirl and I'll let you know how it turns out.


Edit: How did this turn out? FUCKING AMAZINGLY! Thank you!!! This is actually really fun for me to figure out and so satisfying!