We Got A Problem #9: Yearly Multiplication

This Saturday (December 1, 2012) gets written as a short date as 12/1/12 (or, outside the US, generally 1/12/12).  Either way, it’s interesting because 12 x 1 = 12.  That’s happened a lot this year, including June 2.

1. How many times in a century will this happen? It happened once in 2001, twice in 2002.

2. In what year(s) will this happen the most times?  Are there years when it won’t happen?

3. Days like 12/12/44 or 8/25/00 sort of work: 12 x 12 = 144, which you’d write as 44 in a two-digit year.  If you include these days too, how many times in a century does it happen?  Cooool.

On Powerball and Mega Millions

We wrote a lesson in CME Precalculus about lotteries, and used both large multi-state lotteries (Powerball and Mega Millions) as examples — without using their brand names, which would be illegal.

Most of the questions are about how pathetically bad the return-on-investment is for a ticket: try it sometime, it’s amazingly bad when the jackpot value is low.  But eventually the jackpot value grows high enough to make the lottery favorable to the player, right?  Eventually?

This analysis by Jeremy Elson suggests the answer is no, and that when the jackpot is large enough, the mass hysteria of ticket-buying drives the jackpot value down.  When multiple players hit the winning combination, they split the prize, rather than each earning the prize.

And, sure enough, the “$580 million” jackpot was split two ways, with each unfortunate winner only taking a pre-tax cash lump sum of about $175 million.  Only $175 million, what a ripoff!