Trying to find math inside everything else

Posts tagged ‘quadratic’

Potluck Math

I was talking to one of my co-workers about a “Friendsgiving” she is holding, and how the food bill is getting up there as more people are invited. But some of those people are also bringing food – and everyone is worried about having enough.

I realized this is a very common problem with potluck meals. Everyone wants to make sure they have enough food, so the more guests, the more they make. But think about this –

At a 4-person meal, each person makes a dish that feeds 4. (4 servings). So each person then eats 4 servings of food. (Which seems like a normal amount.)

Now it’s a 20 person meal, and each person makes a dish that feeds 20. So now each person eats 20 servings? That seems unlikely – it’s much more likely that people eat 3-6 servings, for 60-120 servings eaten, leaving 80 servings of food left over.

The problem here is that each attendee is treating the problem linearly, when it would better be modeled quadratically. Of course, this is complicated by the one hit dish that every eats a full serving of, and that other dish that no one eats, and everyone wanting to try a little of everything, so figuring out how much to cook can get complicated pretty quickly.

Scrabble Variant

(inspired to post by Anne’s 30-Day Blog Challenge)

So I was playing Scrabble last night (I lost – it’s one of those board games I’m not the best at) when we talked about how, when you are playing with good competent players, the board often winds up with knots of small words close together.

From gamerush.net

Kinda like this one.

So we talked about how we could promote long and fun words instead of those same short words all the time, and thought you could have a variant where you get bonus points based on how long your word is, regardless of which letters you use or where you place it.

Such a bonus somewhat already exists – you get a 50 point bonus if you use all 7 of your tiles. So we thought we could add other bonuses for other lengths. We agreed we should keep the 50 point bonus for 7, and that you shouldn’t get a bonus for only using 1 letter. As well, we thought a 2 tile go should get 1 point as a bonus. So I said I could definitely model it from there.

I tried to feed those data points into Wolfram Alpha for a fit but they provided linear, logarithmic, and period fits, all of which were terrible. I then forced them on a quadratic fit (after all, 3 points make a parabola), which was alright, although maybe too many points for a 6 tile play. Then I did an exponential one (though I had to use (1,0.1) since Wolfram didn’t like using (1,0) in an exponential fit, as if we couldn’t shift the curve down.) Then I just fed them into Desmos and rounded.

Below are the graphs and the tables for each fit. What do you think of this variant? Which point spread would be better? Of course, we’d have to play it to see….

Screen shot 2014-04-26 at 12.17.04 PM