Making my players hate me; introducing Alegebra to the table.

[Toy Killer]

So, in my Class XIX game, the players will be part of a crew that is on a malfunctioning drone ship. Attempting to fix it before it, kills them or anyone else, I'm planning on a little side task to figure out the problem.

The game is dread, and one of the players is actually responsible for the catastrophe on board. I want it to be unknown until towards the end of the game/Story.

I was thinking about having each of the players getting an index card with a number on it, in front of them, Indian Poker style. One of these cards will simply have X on it (Or possibly another letter, but work with me). When the ship starts malfunctioning (A OS error, a Class 19 in the repair codex) they will each get an algebra equation to figure out. I want it so that one has to solve for a variable before the next can be figured out and so fourth until the player with the X can solve for X, which equals 19 (As slang in this setting for a crew member that goes stir crazy is Class 19)... and hope the players catch my drift.

It wasn't until I started trying to write my own equations that I realized this is harder to do then it looks. Any advice, or pointers that I could get for this?

[Gray Mage]

If I'm understanding it right, you want something like this:

I*X=A

Where I is an identity matrix, X is a vector of the variables and A is a vector with the answers.

It'll look something like this (with 3 equations):
{table][1 0 0]||[x1]|=|[a]
[0 1 0]|*|[x2]|=|[b]
[0 0 1]||[x3]|=|[19]
[/table]

Where a and b are arbitrary values and x3 is the last variable you want them to get.

To get an equation with mixed variables, you can add any line to any line, so you can get, for example:

{table][1 0 0]||[x1]|=|[a]
[0 1 0]|*|[x2]|=|[b]
[3 -1 1]||[x3]|=|[3a-b+19]
[/table]

By adding Line 1 to Line 3 and subtracting Line 2 from the result, obtaining:
3*x1-x2+x3=3a-b+19

[Toy Killer]

I think I'm following.

So, with the above example, I could replace x1 with 237, for example, on either side and it won't give away the answer to all five variables?

I'm going to look up Identity matrices here in a second, I promise, but just want to make sure I'm following correctly thus far.

[Gray Mage]

I think I'm following.

So, with the above example, I could replace x1 with 237, for example, on either side and it won't give away the answer to all five variables?

I'm going to look up Identity matrices here in a second, I promise, but just want to make sure I'm following correctly thus far.

The "x" are the answers (your run of the mill x, y, z, etc). A and b are random numbers of your choice that are going to be equal to x1 and x2, respectively because of I. So if a is 237, x1 is 237.

If you mix all of them together, then they're going to need all equations to solve any of them. You can make them solve it by parts, though. Say, if you give two equations, where both have only x1 and x2, they can solve it for x1 and x2, but x3'll remain a mystery until you give a third equation.

An identity matrix is a matrix that has a value of 1 in its main diagonal and 0 everywhere else.

Well, if I'm right you want to make a linear system to be solved. And such a system can be written in the I*X=A form. It's part of linear algebra

Relevant Links: Identity Matrixes; Linear Equation Systems; Linear Algebra Solutions

You can use this last link and backtrack the steps made to get the answer, since you're looking for the question.

[LuckyDee]

Although I don't have any clue about the discussion going on so far, nor would I want it explained to me, I'd like to add this:

It seems to me that what you're doing has nothing to do with your players' characters' abilities, only with the abilities of the players themselves. Any player who is a math wiz in real life but is playing a rough-n-ready space marine (or something along those lines) should actually want nothing to do with your puzzle. The other way around: if the most intelligent character in your group is played by someone who has no knowledge of math whatsoever, they stand no chance of solving your riddle even though they should be the most obvious candidate to do so.

I strongly advocate making in-game/in-character puzzles. Players should be tested through the game, not around it. This is about the same as solving a dispute between characters by a real life game of hide and seek.

If your players are all math wizzes and your campaign has nothing to do with character play, feel free to ignore this of course.

[Sith_Happens]

Any player who is a math wiz in real life brought their graphing calculator to the game.

Fixed that for you. Because I am such a player and would therefore solve this puzzle in about a minute and a half. That's probably for the better, though.

[LuckyDee]

Well, yes and no. But I see your point.

[Gray Mage]

Fixed that for you. Because I am such a player and would therefore solve this puzzle in about a minute and a half. That's probably for the better, though.

Or anyone that has acess to WolframAlpha. It might be a bit tricky to type in a cellphone if there isn't a computer available, but it's doable.

Edit: One piece of advice I think is usefull for puzzles in games is that it shouldn't be mandatory for the party to solve them. So in this case, it provides a good clue as to what happened, but it shouldn't be vital, just a bonus.

[Flickerdart]

Is alegebra algebra for dwarves?

[TuggyNE]

Is alegebra algebra for dwarves?

Yes. Yes it is.

[NichG]

'Challenge the players' is a perfectly valid style of play. So long as thats the accepted framework of his game, there's nothing wrong with this.

The real problem is that if we're talking a matrix of linear equations, there's nothing stopping someone from solving it symbolically before they have numbers to plug in. If you really want things where 'how you solve it' depends on another person's piece of the puzzle, you need something nonlinear. That starts to push the bounds of what I'd expect the average group of players to be comfortable dealing with.

But here's a concrete example with two equations, just to give you an idea.

Eq1: x^2 + xy = 3
Eq2: y^2 + x^2 y = 2

If I have Eq1, I can find that y = (3-x^2)/x immediately
If I have Eq2, I can find that x = ((2-y^2)/y)^(1/2) immediately

But because its nonlinear, those aren't the best ways to solve the combined equations. Doing that reduction doesn't actually help me with the final problem, because if I just plug x or y into the other equation I'm going to get a rats nest that still needs to be untangled. For example, plugging the 'x' solution into the 'y' solution gets the equation:

y = (3- (2-y^2) / y)/( (2-y^2)/y)^1/2

Which is still a mess. Most of the work remains to be done but now, having both equations, you can finally move to a solution:

y ( 2-y^2) = (3-(2-y^2)/y)^2

2 y^3- y^5 = 9 - (4+y^4-4*y^2) - 6*y*(2-y^2)

And now even for this simple problem you have a fifth order polynomial. I didn't check if this one is easily factored, but if it isn't then you're out of luck here (I mean, you can solve it numerically, but not on paper anymore).

So you can see how bad this can get.

Edit: Here's a nicer one you can actually solve

x^3 y^2 + xy = 3
x + x^2 y = 2

The substitution 'z=x^2 y' turns out to be convenient when you multiply the top equation by 'x'.

[LuckyDee]

'Challenge the players' is a perfectly valid style of play. So long as thats the accepted framework of his game, there's nothing wrong with this.

I'm not denying this - although I must admit that I'm not a fan of the concept. I'm merely pointing out that in this case the discrepancy between what constitutes a challenge for a player and what for a character is potentially humongous.
Mind you, I come from a background that focuses on story driven gameplay. Were I to translate the scenario given in the OP to any of the campaigns I've ever run, not only would the puzzle not get solved, it'd also be severely out of place and would only serve to diminish the story rather than enhance it.

I'll reiterate: if both all players and all characters are this good at math, you (ie. the storyteller) are making an excellent choice. If the characters aren't but the players are, and it's part of the framework, fine again.
If either not all players or not all characters are wizkids, I would advise against this course of actions, and encourage a puzzle more suitable for the group. Since the OP is unclear about a lot but hints at a strong link to the background and story, I got curious.

[Gray Mage]

Well, if you do get to do this, let us know how it turns out.

[erikun]

So do you want to force everyone to solve round-robin before the final player solves for X, or do you want each player to solve their own problem independently, and then use those values to solve for X?

For the first one, I would just put down some simple algebrea equations, but the second one requiring the solution to the first, the third requiring the solution to the second, and so on. I'd probably label the variable in the first problem as alpha (α), the variable in the second as beta (β), and so no to indicate the process we're looking for. As an example:

α² - 2α = -1 (First problem, solution α = 1)
β/5 = 2α + 3 (Second problem, β = 25)
χ = β - 6 (Last problem, χ = 19)

The other method, where everyone else solved and puts it together in the final equation, would look like this:

α² - 2α = -1 (First problem, solution α = 1)
β/5 + β = 30 (Second problem, β = 25)
χ = β - 6α (Last problem, χ = 19)

[Toy Killer]

Well, I want a theme of Team work and working together ringing through the game. I even am going to allow one player to pull on behalf of another, which is outside the rules of Dread, but I think it could have an effect.

Either way, the Algebra is simply a side thing the players can do to ease the fixing of the ship, as the crew members are deliberately redundant for that purpose.

The whole point is that when the equation is put together, they feel 'Techy', doing busy work (Fitting of the game setting) and in game tension will pull them away from fixing the malfunctioning ship as the game progresses.

Realizing the Programming officer (who has the largest equation to figure out) has been crazy will pull all the lose threads together. Now, they could manage to fix the ship without the equation, but I think seeing that one player has X for their Indian Poker index card and the player announcing that X = 19, the players will be familiar with Class 19s to put together the programming officer had intentionally/unintentionally sabotaged the ship.

[NichG]

Instead of a bunch of algebraic equations, why not make it a circuit diagram puzzle? Phrase it in terms of things like 'when this valve is open, this other valve must be closed or coolant will leak into the cabin', and then have the players construct it using logic tables/logic gates/whatever they like.

Crunching numbers won't feel techy, it'll feel tedious; its the modern era, we have calculators for that kind of thing. I remember at one point I was in a 1ed D&D campaign where the DM pulled a 'balance the weights' type puzzle from a book of tricks and traps. It basically required inverting a 7x7 matrix. We all knew we could do it, but none of us wanted to actually bother.

[Delta]

This sounds like a fun idea IF you know all your players enjoy math and have at least a reasonably working knowledge of the level of math you're asking of them. That is a big if, but if you're sure of that, I say go for that, otherwise stay the hell away. Unfortunately, it's completely socially accepted to completely ignore math and forget what little you absolutely have to learn in school the minute you leave, so a lot of people have no math skills whatsoever and would feel completely discouraged when looking at a puzzle like this.

That's why your usual "player challenge" puzzle is based on either simple geometry (because anyone can puzzle with actual puzzle pieces he can push around) or basic logic (because in the end, no one can claim that he was missing some learned skill to find out who lives in the red house)

So it all comes down to "know your players"

[Alejandro]

Remember, the game must be able to proceed if no one solves the puzzle. Never use a puzzle whose correct solution is mandatory for the game to proceed, because eventually the players either will be unable to solve it, or not interested in solving it, and your game breaks.

[magwaaf]

So, in my Class XIX game, the players will be part of a crew that is on a malfunctioning drone ship. Attempting to fix it before it, kills them or anyone else, I'm planning on a little side task to figure out the problem.

The game is dread, and one of the players is actually responsible for the catastrophe on board. I want it to be unknown until towards the end of the game/Story.

I was thinking about having each of the players getting an index card with a number on it, in front of them, Indian Poker style. One of these cards will simply have X on it (Or possibly another letter, but work with me). When the ship starts malfunctioning (A OS error, a Class 19 in the repair codex) they will each get an algebra equation to figure out. I want it so that one has to solve for a variable before the next can be figured out and so fourth until the player with the X can solve for X, which equals 19 (As slang in this setting for a crew member that goes stir crazy is Class 19)... and hope the players catch my drift.

It wasn't until I started trying to write my own equations that I realized this is harder to do then it looks. Any advice, or pointers that I could get for this?

what's that in english?