Mathematics

[johndallman]

Originally Posted by Brandy

I think that the inspired/versitile solution would be:
"Each person shakes hands with 18 other people. That would be 18x20=360 handshakes, but I've counted each handshake twice. Therefore the answer is 360/2=180."

I think that's actually the method of some one who's learned to "think with numbers." This is only loosely connected to Mathematics skill: engineers usually have it, but professional mathematicians are often much better at picking up new systems of formal logic and applying them than they are exploiting the natural numbers. I am not a mathematician, but I work with them.

[Hide]

Originally Posted by Fred Brackin

Person 1 is married to Person 2 and therefore begins shaking hands with Person 3. When you start to count Person 3's handshakes you've already counted his shaking hands with Person 1.

Originally Posted by Brandy

I was at the party, and so was Mr. Smith. When I counted 18 handshakes for each of us, I included my handshake with Mr. Smith in his count and in mine.

Ha! Ninja'd by Fred.

Oh, that's right! Clear as mud.

Thank you both!

[kdtipa]

Originally Posted by Hide

I know the answer is right, but what's the logic behind "I counted each handshake twice"? What's the "dupe" handshake?

The initial count is the number of people involved, but two people create one handshake.

[Brandy]

Originally Posted by johndallman

I think that's actually the method of some one who's learned to "think with numbers." This is only loosely connected to Mathematics skill: engineers usually have it, but professional mathematicians are often much better at picking up new systems of formal logic and applying them than they are exploiting the natural numbers. I am not a mathematician, but I work with them.

I agree with all of this. Quantitative reasoning shouldn't be thought of as limited to people with the Mathematics skill.

[kdtipa]

Originally Posted by coronatiger

If a low-tech character needs to figure out a maths puzzle, how would you model it? Assume the character doesn't have Mathematics skill.

Example: Ten married couples meet at a party. How many handshakes will there be if everyone shakes hands with everyone but their own spouses?

Edit: What should be the probability of an untrained person figuring out the correct answer?

To answer how I would handle it, I think I'd back up a step. Why is there a puzzle like the one you described? Puzzles like that in a role-playing game tend to be the "break the 4th wall" kind to give players something different to do in my experience. If you spend the time to create a puzzle, it's for the players, not the characters (again, in my experience).

If the puzzle is purely in game and there's no actual definition for it, that's when I'd look for rolls based on the characters. If the cook needs to know how many chickens to kill to make enough meat for 23 people... I'll let the player roll (either against Mathematics or the default) to see if they figure it out correctly. It doesn't matter what the right answer is... just whether the character figured it out.

So, if it's a puzzle (math or not) that I found or put together that has a specific answer that could be figured out... I'll let the players do that, and there won't be any rolls at all. If it's a puzzle for the characters and the answer doesn't technically matter: I'll let the players roll.

[Hide]

If this is a person with very basic math knowledge, I would think the easiest is doing something like this:

O 1 2 3 04 5 6 7 8 9 A B C D E F G H _I J K
1 X X X X X X X X X X X X X X X X X X X X
2 X X X X X X X X X X X X X X X X X X X X
3 H H X X X X X X X X X X X X X X X X X X
4 H H X X X X X X X X X X X X X X X X X X
5 H H H H X X X X X X X X X X X X X X X X
6 H H H H X X X X X X X X X X X X X X X X
7 H H H H H H X X X X X X X X X X X X X X
8 H H H H H H X X X X X X X X X X X X X X
9 H H H H H H H H X X X X X X X X X X X X
A H H H H H H H H X X X X X X X X X X X X
B H H H H H H H H H H X X X X X X X X X X
C H H H H H H H H H H X X X X X X X X X X
D H H H H H H H H H H H H X X X X X X X X
E H H H H H H H H H H H H X X X X X X X X
F H H H H H H H H H H H H H H X X X X X X
G H H H H H H H H H H H H H H X X X X X X
H H H H H H H H H H H H H H H H H X X X X
I H H H H H H H H H H H H H H H H X X X X
J H H H H H H H H H H H H H H H H H H X X
K H H H H H H H H H H H H H H H H H H X X

If you add the letters "H" per column, you get:

18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 0 0

Which sums 180.

[Hide]

Originally Posted by kdtipa

So, if it's a puzzle (math or not) that I found or put together that has a specific answer that could be figured out... I'll let the players do that, and there won't be any rolls at all. If it's a puzzle for the characters and the answer doesn't technically matter: I'll let the players roll.

I would do something similar; also I would do it if the players could not solve the puzzle (as last resort).

[Anthony]

Incidentally, this is a /TL situation, while this is grade school math for us, it's not something most people would have any idea how to solve at TL 4 or less.

[whswhs]

In low-tech societies, it depends on how they approach arithmetic. If they have no notation at all, they may not be able to do i, unless it's simple enough for counting on their fingers. If they have nonpositional notation (like traditional Chinese numerals or Roman numerals), they can write down the answer, but doing the problem takes either the use of an abacus, or a roll vs. Mathematics (Applied). If they have positional notation, doing the calculation is no worse than an IQ roll (and I'd probably let a player get away with doing it in their head, unless their character had some mathematical disability), but figuring out how to set it up would probably be a Mathematics (Applied) roll at default.

There's more about this in GURPS Low-Tech—chapter 3, I think.

[whswhs]

Originally Posted by Anthony

Incidentally, this is a /TL situation, while this is grade school math for us, it's not something most people would have any idea how to solve at TL 4 or less.

Yes. I copy edited a study of Pascal's early work on probability theory, before he published. He had the problem of figuring the odds of different dice rolls. So he said "2, 1+1, one chance; 3, 1+2, one chance; 4, 1+3 or 2+2, two chances; 5, 1+4 or 2+3, two chances. . . . " This was a really brilliant guy, but it wasn't obvious to him right away that 1+2 and 2+1 were two different ways to roll a 3.