## Thursday, November 21, 2013

### Paid in Full?

Posting an idea for a mini math project so I don't forget it and to let other people play with:

In the recent lawsuit of Apple v. Samsung an urban myth has sprung up that Samsung decided to pay a 1 billion dollar fine with a bunch of 5 cent coins. Why the article is calling them 5 cent coins instead of, you know, nickels, I dunno.

First off, let's ask if this is a realistic number. I started by looking at how many nickels are minted annually given I don't know what other 5 cent coins they could be talking about. It fluctuates, so I added up the past few years and took an average to try to get a rough idea. Between 2007 and the data they had for 2011, it averaged out to about 750 million a year. Glancing back a few more years that looks like a pretty decent average so I stopped there. But if that's the case, you'd be looking at 100% of the nickels minted for 13 years being entirely dedicated to this payment. Sounds pretty sketchy.

But let's go with it. Let's say someone dumped off what was supposedly a billion dollars worth of nickels and you're in charge of making sure you've been paid in full. A lot of commentors on the article are saying to weigh it and divide by the weight of a single nickel. Doesn't sound so hard but there's a few catches. The first is in the sensitivity of instruments. Getting devices that can weigh several tons with a precision of tenths to hundredths of grams is not likely.

But for the sake of argument we'll pretend everyone has such a device and it's no problem. Another issue is that due to wear some weight of coins could be lost. Due to gum or other residue, the weight of the coins could be increased. Thus, unless the coins walked right out of the mint and into the supposed hands of Apple, weight will have some small variance to it. Small, but multiplied by 20 billion, small numbers tend to get rather large.

So here's the project. Get a bunch of nickels and weigh them up, build a histogram, fit a bell curve to it and determine the standard deviation. For a few standard deviations in either directions, determine how much you may have been over or underpaid.

Other ideas: The article states it took 30 trucks to deliver the supposed coins. The amount this would actually weigh would far exceed the capacity of any trucks out there, even split 30 ways. So estimate how many trucks it really would take.