October 15, 2007

I break (4) math.

On Friday, in a strange and reckless mood only heightened by the absence of anyone in my office to pay attention to me, I spent my afternoon break attempting to logically estimate the total weight of the Empire State Building. I used a piece of notebook paper, a pen, and a series of wildly inaccurate assumptions, and I eventually came up with a figure which was almost exactly 1% of the correct number. So said my post-project internet research, anyway. I invite you to, without looking up any dimensions or statistics, post any guesses, calculations, or wild hypotheses that you may have.

Beware, though; math may not be functioning to normal standards at the moment. Consider:

  • The infuriating pattern-matching game Set contains a deck of precisely 81 cards.
  • 81 is a number divisible by 3. This is a well-known feature of the number 81.
  • This divisibility by 3 is what makes gameplay -- consisting of picking up sets of exactly 3 cards -- possible.
  • Last night, when Katie and I played the game, we ended up with 9 cards that could not be made into sets. This is not a problem.
  • When we checked through our sets, however, Katie had one set of 4. That IS a problem.
  • With one set of four, we could not possibly have had a divisible-by-3 number of cards remaining.
  • Every other set was a set of 3. There were no sets of two, no sets of five, and no other sets of four.
  • Three, three, three, three, three, three, three, four, nine.
  • No number of threes will make that sum to 81.
  • When we shuffled and counted the cards there were precisely 81.
  • Three, three, three, three, three, three, three, four, nine. Eighty-one. It's mathematically impossible.

All we could really do was give each other frightened looks, agree that we had somehow broken basic arithmetic, and go quickly to bed to try to forget about it.

Posted by dianna at October 15, 2007 02:19 PM

Heads. Heads. Heads. Heads. Heads.

Posted by: didofoot at October 15, 2007 02:37 PM

That's more or less exactly what I'm afraid of. If anyone gives me any sealed letters, I am throwing them right overboard.

Posted by: Dianna at October 15, 2007 02:59 PM

Marry, nuncle, methinks our fate is Set.

Posted by: didofoot at October 15, 2007 03:05 PM

...Ah. Well played, madam.

Posted by: Dianna at October 15, 2007 03:31 PM

Hmmm.. Empire state Building. Let's see. It's got to have about a 100 floors. The majority of weight should come from concrete. The largest concrete block I have seen a worker lift was about 10 cms thick and half a meter square. That must have weighed at least 40 kg. So, .05m^3 concrete is 40 kg. So a m^3 of concrete should be 800 kg. Now that sounds a bit less. They must use some high density crap in Empire state building so, I will put it a t 1000kg/m^3 and slightly underestimate the volume of concrete on one floor. One floor should at least be 3 meters high and should have at least 20 m^2 worth of pure concrete on it. Make that 40. This is the empire state. But they would want to be light and flexible on the top. I will settle for around 35. So we have around 100 m^3 of concrete on one floor. So, my guesstimate is 100,000 Kg. Sounds less... Am I anywhere close?

Posted by: Anshul at October 16, 2007 03:28 AM

Oooh. See, you did the same thing as I did -- start with one spot-on assumption and then drastically undercalculate from it. Nice!

Should I tell you what percent of the actual figure you have arrived at, or would that spoil things for future guessers?

Posted by: Dianna at October 16, 2007 09:53 AM