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Subject: Need help with the maths. rss

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Michael M.
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I've spent about an hour trying to crack this, and being particularly bad with math, I haven't. So, I figure I'd reach out to you guys for some assistance. Basically, there are twenty characters broken into four "classes," five in each class.



Each character has two "friends," and these friends are also from the same pool of characters. The twenty characters are from the same pool as the "main characters." However, I keep ending up in situations where there isn't exactly two friends for each character.



I've tried adding a sixth character to each class, that didn't help. I tried a few other things out, nothing seemed to make it line up exactly. The game is in a VERY early stage, so I'm not really married to anything about it yet. I can add a class, reduce the number of people per class, etc... all those are viable options. The only thing I would be hesitant to change is the number of friends each player has, since two is perfect for my purposes. Suggestions?
 
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DZ Woloshyn
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You've got all of the people essentially divided into groups of 3 such that no two friends come from the same class. With 20 people, that won't work: you'll need a combination of members and classes that combines to be is divisible by 3. For example:

3 classes, 6 members each = 18 total, 6 groups
4 classes, 3 members each = 12 total, 4 groups
4 classes, 6 members each = 24 total, 8 groups
6 classes, 4 members each = 24 total, 8 groups

Example: add Fritz (green), Chubby (blue), Murph (pink), and Otho (yellow) to your classes. Without much thought, I can get...
d10-1alexG, frankB, kentP
d10-2brandonG, rickyY, gabeB
d10-3connorG, mattP, steveY
d10-4derekG, ignacioB, nateP
d10-5eddieG, victory, johnnyB
d10-6fritzG, murphP, zackY
d10-7lanceP, quintinY, howieB
d10-8peterP, chubbyB, othoY

With 6 (or some other even number) per group, perhaps you might also be able to match members within a group into 3 pairs of rivals...?

Best of luck!
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T. Dauphin
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Just needs a little rearranging;

I took Johnny off of Derek's friend list, replaced him with Eddie.
Move Johnny to Peter.
So now;

Derek...Zack...Johnny
Eddie...Peter...Derek
Johnny...Zack...Peter
Peter...Eddie...Johhny

Unless you have some other criteria for match ups...

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Byron S
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Do these groups of friends all have to be friends with each other? If friends of friends don't have to also be friends, it's not hard.

ZAFKQBGLRCHMSDINVEJPZA

Alex is friends with Zack and Frank, Frank is friends with Alex and Kent, etc.
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Allan Morstein
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Quote:
Do these groups of friends all have to be friends with each other? If friends of friends don't have to also be friends, it's not hard.

ZAFKQBGLRCHMSDINVEJPZA

Alex is friends with Zack and Frank, Frank is friends with Alex and Kent, etc.


There is an unstated requirement that each set of three friends must all have the same friends. For instance, if Zack/Alex/Frank are friends, then none of those three can have any other friends. This is pretty clear from the data, though it isn't specifically stated in the problem.
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Andrew Meadow
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You need a number of characters divisible by three. Add one more character of any class (or maybe a hybrid of two classes?). Problem solved.
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Michael M.
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alkamo wrote:
Quote:
Do these groups of friends all have to be friends with each other? If friends of friends don't have to also be friends, it's not hard.

ZAFKQBGLRCHMSDINVEJPZA

Alex is friends with Zack and Frank, Frank is friends with Alex and Kent, etc.


There is an unstated requirement that each set of three friends must all have the same friends. For instance, if Zack/Alex/Frank are friends, then none of those three can have any other friends. This is pretty clear from the data, though it isn't specifically stated in the problem.


You're right, I was thinking in terms of groups of three for friends. But I wonder if that really is necessary. It would provide more variety if friends of friends didn't have to be friends. Hmmm...
 
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Michael M.
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Another thing is that I'm going to have another 20 characters who are female characters and do the same thing. Once I have the basics down, though, I'd like to have some guys with female friends and some girls with guy friends. I'm not sure exactly what the ratios should be yet though.
 
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Jeremy Lennert
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There also seems to be an unstated assumption that your friends can't have the same class as you.

You should really try to state all of your requirements up front. It's plain unreasonable to expect anyone to solve your problem if you can't even tell us what counts as a solution.


The requirement that friendship is mutual means that you're effectively grouping people into clusters of 3, which means the total number of people obviously has to be a multiple of 3. Since your number of classes is coprime with 3, that means the number of people per class also must be a multiple of 3 (unless you change the number of classes, or have an unequal number of people per class).

The requirement that no two friends can be from the same class means that no single class can have more people than there are groups (i.e. no more than 1/3 of the total people). You already meet that requirement.

Once you fix the multiple-of-3 thing, you'll probably find this is pretty easy...unless you have any other requirements you haven't told us.


Have you been playing Renowned Explorers: International Society? They have 4 classes with 5 characters in each class and every character has a recommended party of 2 other characters (of different classes) to send with them if you choose them as a captain. Their recommendations aren't entirely symmetric though (as already noted, they can't be, because the total number of characters isn't divisible by 3).
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Michael M.
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Sorry if my first post wasn't very comprehensive. I didn't want to overwhelm everyone with a full on explanation of the game and every requirement. I was just having a hard time figuring out that particular problem, not trying to start a W.I.P. thread. But I understand now that more information is better than less, so I get where you're coming from. Also, I haven't played (or even heard of) Renowned Explorers. I should probably check it out.

But, here's an explanation of what I've titled "Dance Card"

The setting of the game is a high school dance, such as homecoming or prom. The board will be a top down view of an area decorated as a dance floor, either the auditorium or the indoor basketball court. There will be four main "spaces," marked A, B, C and D, that characters will occupy, and a few side areas that I don't need to go into right now. The objective of the game is to successfully dance with three predetermined characters on the board before the other players do. You can dance with a character by moving into the section they are currently in, then rolling a d6. If you a roll a 5 or 6, they accept your invitation and dance. If not, you strike out and have to go dance with someone else and hopefully rebuild your dance cred. Of course, you can increase your chances by finding and talking to the best friends of the people you're trying to dance with, having your friends come along and providing encouragement, and making sure there aren't any other flashy dancers there to distract them.



There are twenty four characters, each represented in two ways. First, they have a little cardboard standee, ala Dead of Winter or Arkham Horror. Then, each character also has a card, their Dance Card, with information on it. At the the beginning of the game, the players randomly place six characters in each of the four spaces, so that all twenty four are on the board. Then, each player randomly draws one of the dance cards, which will tell them which one of the characters on the board is them.

(Tarot sized)

This is where the question of how to arrange the characters in my OP comes in. Each of the twenty four characters will have a dance card that looks like the above. Above the dark black line is your character portrait, showing you which of the characters on the board you are. If there is any special ability it will be listed there. Then will be two smaller portraits of your two friends, and then a portrait of your rival. Friends add +1 to your dance roll if they are in the same space as you and the character you are trying to dance with. Rivals deduct -2 from your roll if they are in the same space. And yes, other players may draw a character that ends up being your friend or a rival, which makes things very interesting.

Each player has three potential dance partners they need to complete dances with. These partners are listed on your dance card. To the right of their portraits will be a list of their friends, which you can speak and get advice from, giving you +1 for each "Advice" token they give you when you attempt to woo their friend. However, instead of rivals, your dance partner's have crushes. This means that if your potential partner is in the same space as their crush, they won't even give you the time of day! You're gonna need to maneuver them to a part of the dance floor where you're all they see!

The other important factor in the game are the "Classes," though I need a different name for them. There are four classes, represented by a colored border on the characters.

Green = Smooth Moves
Blue = Confident
Yellow = Funny
Purple = Romantic

Each potential dance partner has a "distracted by" class. This means you suffer -1 to your dance roll for each character of the class in your space, since they're distracting the girl/guy whose attention you're trying to get. The two ways to get around this is to either maneuver them away or learn some skills to use on them. Each of your friends is a different class than you, so you can speak to your friends to gain a token that will allow you to count as both that class as well as your original class. That way, he/she won't be distracted by anyone else!

On any given turn, each player can move to a new space on the dance board, and can choose to speak to a friend to learn a skill, speak to a friend of someone on your dance card to gain +1 when performing a dance roll with that potential dancer, or, speak to the potential dancer and make the roll, either causing you to strike out or successfully dance with them!

These are the basics. I'm also thinking that every time all the players have gone (a full round), there will be a deck of cards, lets call it the event deck, and you have to flip over the top card and do what it says. It will say things like "Move all Romantic dancers clockwise one space. Move all Smooth Moves dancers counter clockwise one space." or something like that. Also figure there will be a few difference categories of song, such as "Hip-Hop," "Rock," "Techno," "Throwback," "Slow Jam," etc... that will be printed on each of these event cards, and certain characters will be easier to dance with when the kind of music they like is playing. For example, if one of your potential dance partners is Katie, it may say on her section of your dance card that she likes Slow James. When the current event card indicates that a slow jam is playing, you gain +1 to your roll.

So that's my general idea for the game. A light, fun theme with a relatively simple mechanic.
 
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Jeremy Lennert
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M_Strauss wrote:
Sorry if my first post wasn't very comprehensive. I didn't want to overwhelm everyone with a full on explanation of the game and every requirement. I was just having a hard time figuring out that particular problem, not trying to start a W.I.P. thread. But I understand now that more information is better than less, so I get where you're coming from.

That's not it. If you dive into details of how your game works that aren't related to the original question (like you just did), that's more likely to make me give up and read a shorter thread than it is to help me answer your question.

But you need to provide the relevant details.

Imagine I posted a thread that said something like, "Hey, I'm trying to add 27 and some other number, but I can't figure out what the sum should be. Can anyone tell me the answer?"

Then I get replies that say "Uh...we can't tell you the sum unless you tell us both of the numbers you're trying to add. Just 27 by itself isn't enough to figure out the answer."

So then I say "Sorry for not providing more context. You see, I'm developing a game about telephone manufacturing where you have to..." and then go on for 3 pages about how my game works.

That's not helping. That's just going to make readers who would have helped me impatient.

If you just say "I have 20 people (A through T) and each of them needs 2 friends from the same list of people," then you should reasonably expect someone to reply "Easy. A is friends with A and B. B is friends with A and B. C is friends with A and B. D is friends with A and B. And so on."

That correctly answered your question, but it won't help you, because what you asked isn't the same as what you wanted.

Don't provide irrelevant background, but do ask for what you actually want. Explain the constraints that limit what kind of solutions you can accept. (You usually shouldn't explain why you need to follow those constraints, just mathematically what they are.) Things like "Friendships must be symmetric and transitive, all friendships must be to a person in a different class, all people must have the same amount of friends."
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Clay Hales
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I'm still not sure what you are getting at. There are the 20 people distributed among 4 classes that each need 2 friends. The number per class and number of classes could change, but the 2 friends is kind of set. For lack of a better term this group of character and 2 friends is a 3 person team.

Are these teams exclusive? In other words, do the primary character and the two friends only show up in one team? If so, like said before there needs to be a population that is a multiple of 3. 6 each per class will do this.

Do the classes matter in the make up of the team? Can there be 2 or 3 from the same class that are in one team? For that matter can the enemies/rivals be in the same class as the primary character? Have to be in an different class? Have to be in a class not present in friends?

From what I can gather from the description of the game (assuming exclusive teams and the only restriction for rivals being they can't also be one of the friends in the team), I would just say to have the total population of people be three times the maximum number of players, and friends/enemies determined by card draw. IF the whole population is on the board with less than the maximum number of players, make sure the population is AT LEAST three times the maximum number of players.

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Michael M.
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Antistone wrote:
That correctly answered your question, but it won't help you, because what you asked isn't the same as what you wanted.

Don't provide irrelevant background, but do ask for what you actually want. Explain the constraints that limit what kind of solutions you can accept. (You usually shouldn't explain why you need to follow those constraints, just mathematically what they are.) Things like "Friendships must be symmetric and transitive, all friendships must be to a person in a different class, all people must have the same amount of friends."


I believe you're right, and I'll try to be better at that in the future. The good thing is that I got the answer I needed anyway, but I definitely could have been more specific and given the proper details.
 
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