It's That Time of Year Again

It's that time of year again.  The holidays are here, and you can't flip through the channels without eventually hitting a Christmas special.  We watched Miracle on 34th Street yesterday, and I was struck by the scene at the end where all the mail addressed to Santa gets shipped to the courtroom where Kris Kringle is on trial. One of the clerks in the mail room says "there must be about 50,000" letters to Santa Claus that they have to get rid of.  How many letters get delivered to the court room?

In the movie, 21 duffel bags full of letters are brought in and dumped on the judge's desk.  Judging by how the men carry the bags, they certainly weigh between 2 and 200 lbs, so we can reasonable assume there are about 20 lbs of letters to Santa in each bag.  According to the United States Postal website, a standard letter weighs less than 3.5 ounces.  Assuming a 1 ounce letter, we can easily compute the number of letters delivered,

# of letter = (21 bags) × (20 lbs/bag) × (16 ounces/lb) / (1 ounce/letter)

= 7000 letters.

At about 7000 letters, the mail clerk was correct to within about an order of magnitude.  Not too shabby.