## Trying to find math inside everything else

### Groceries and Gas

Here’s a topic that came up in conversation during Easter dinner tonight. I thought that there could be some interesting math involved, so I’ll present it Problem of the Week style, with no question or prompt.

At the S&S grocery store, there is also a gas station. If you buy \$100 worth of groceries, you get \$0.10 off of each gallon of gas. You can save those up – so, for example, if you eventually buy \$300 worth of groceries, you’ll have \$0.30 off each gallon.

Right now, gas costs \$2.20 per gallon. You’re even allowed to bring gas cans to fill up when you buy, but the maximum is 35 gallons in a single purchase.

What do you notice? What do you wonder?

### The Math of Bedroom Compatibility

On OKCupid, one of the match questions is the following:

“Once you are intimate, how often would you and your significant other have sex?

– Every day
– About every other day
– Once or twice a week

– A few times a month or less”

On OKCupid, you choose your own answer and then pick what answer you’d like potential matches to answer. It seems straight-forward – if the other person picks the same answer as you, it’ll be fine. But will it?

Let’s make the following assumptions.

• A person is either in the mood to have sex on a given day, or they are not.
• Two people only have sex if both are in the mood.
• If someone is in the mood and has sex, they are happy. If they are not in the mood and don’t have sex, they are happy.
• If someone is in the mood and does not have sex, then they are unhappy.

If both people choose “Every Day,” then it will be fine; both people will be happy every day.

If both people choose “Every other day,” let’s assume they are in the mood 4/7 days of the week. So on a given day, there is a 4/7 chance of being in the mood.

It follows, then, that on any given day the chance of both people being in the mood is 16/49, or ~32.65%. And so the probability of having sex 4/7 a week is 7C4*(0.3265)^4 * (0.6735)^3 = 12.15%.

So that’s an 88% chance of not being satisfied in a given week. Well, that didn’t work out.

(Of course, the assumptions aren’t perfect – mostly because being in the mood might carry over if the itch wasn’t scratched.)

### The Cold War

In my first year teaching I came up with this activity for working with quadratic-linear systems, based in the Cold War and missile defense. It didn’t work as well as I hoped, mostly because it was too complicated, but I like the core of the idea. Maybe now, with more experience and the brainstorming power of the MTBoS, we can think of a way to make it work. But first, I’ll describe what .i actually did.

Students entered the room to find the desks rearranged – four big group tables, and the room split down the middle by a wall of desks, representing the “Iron Curtain.” Each student was then randomly assigned to one of four groups: US Missile Command, US Missile Defense, USSR Missile Command, and USSR Missile Defense. (Only one student, the son of the Georgian consulate, demanded to be switched from the USSR group to the US side.)

Each student then had two roles – one of the roles was their job on the team. Treasurer, secretary, chief engineer, etc. These roles were public. Their other roles were secret – they were things like Double Agent, Handler, FBI Agent, Innocent.

The idea was that each missile team was trying to build a missile that could hit the other country, while bypassing their missile defense. And the missile defense teams were trying to shoot down the missiles. The missiles were represented by quadratic equations and the missile defense by linear functions. But the best way to find out what the other side was planning is through espionage.

Of course, the thing they’ll probably learn is that the missile defense fails and everyone dies – we all lose the cold war.

Below are the files I made way back when. What are your ideas to make this workable?

### Weight on Other Planets

I took some photos today at the AMNH with their scales with the intention of posting them as Estimation180-type challenges. I realize as I review the photos, though, that there were some issues. The numbers fluctuated a lot when I stood on the scales, so the pictures I have vary by a huge margin (+/- 30 pounds to my Earth-weight). They didn’t fluctuate when I put my bag on, but not every scale register its existence.

Estimation #1 – Here’s my bag (laptop, iPad, book, charger, 3DS). How much does it way?