Jelly-goodness

March 22, 2005 11:05 AM

The management of my office building is holding a contest: determine the number of jelly beans in a container. Prize: $500 at Best Buy and all the beans.

I need some math gurus to give me pointers on how to figure this out. The beans are in a bowl shaped like a half circle. This bowl is sitting inside a square plexiglass display case with a couple of inches to spare on each side. I haven't taken any measurements yet, but will probably mosey on down shortly. The beans appear to be of a standard size, but there are some that are misshaped.

Oh, and they only want the number of pink jelly beans.

Suggestions on how to calculate this?

posted by smcniven to grab bag (12 comments total)

As per The Wisdom of Crowds by James Surowiecki, the average of all of the employees' guesses will be closest to the real number.
posted by matildaben at 11:08 AM on March 22, 2005

Weigh a counted amount of the same jelly beans, say, 100 of them. Weigh the same glass bowl (you shouldn't have a hard time finding one at a shop nearby, I bet), and weigh the same amount and thickness of plexiglass (home depot ahoy!).

Check how many pink jellybeans there are in that 100, and then mix them up again, do this a few times until you get an average number of pink jellybeans per gram.

Weigh the display, subtract the glass(es), and you should be pretty much dead on.

Enjoy your best buy certificate, it probably cost you $10 in jellybeans. :-D

[Cheating is fun when you use your brain about it!]
posted by shepd at 11:13 AM on March 22, 2005

make sure to subtract the weight of the baseball that's surely hidden away in the center of the bowl to keep you from cheating.
posted by fishfucker at 11:16 AM on March 22, 2005

cheating, in this case, meaning making a guess that you can reasonably expect to be accurate.

STOP COUNTING CARDS>
posted by fishfucker at 11:17 AM on March 22, 2005

make sure to subtract the weight of the baseball that's surely hidden away in the center of the bowl to keep you from cheating.

Unless the asker works at Google, nobody's going to be that clever.
posted by Saucy Intruder at 11:34 AM on March 22, 2005

Buy a package of jellybeans. Let:

n = the number of pink beans.
v = the volume of all the beans.

Mosey on over to the bowl. I'm assuming it's shape can be approximated by a Spherical Frustum. Estimate the following dimensions:

b = the diameter of the base
h = the height of the bowl
a = the diameter of the opening

The volume of the bowl is roughly:
V = (1/6)pi*h(3a² + 3b² + h²)

The number of pink beans should be:
nV/v
posted by Eamon at 12:25 PM on March 22, 2005

D'oh! Make those the radius of the base and opening. Sorry about that.
posted by Eamon at 12:38 PM on March 22, 2005

I second the idea of:

1) Measure the bowl and get a bowl of the same size
2) Measure the beans and buy bags of beans the same size

Do this at home and use that as your estimate.

As for, getting only the pink ones, you cant count on having the same "mixture" as them but you can derive a

visiblepink/totalpink ratio using any color from your own bag. Then go back and apply that ratio to the visible pink beans from the jar to be guessed at.

This is one of those cases wher I would not use mathematics. just street smarts.
posted by vacapinta at 12:50 PM on March 22, 2005

1. Eyeball how many jellybeans there are.
2. Buy 401 tickets, each one a different number ranging from your guess -200 to your guess +200
3. Win the $500 and pocket $99.

Now, was that very fun? I didn't think so.
posted by furtive at 1:34 PM on March 22, 2005

Go in early or stay late. Raise the plexiglass box, spill out the beans, count the pink ones, replace beans, replace box.
posted by substrate at 3:11 PM on March 22, 2005

Hire Diebold or ES&S to count the pink beans.
posted by weapons-grade pandemonium at 5:18 PM on March 22, 2005

Well, I did some measurements, figured out the rough radius of the bowl, rough volume of a jelly bean and estimated that pink beans were about 20 percent of the total. My guess: 1186 beans.

I'm tempted to give best answer to substrate though. Did you peel the stickers off your rubiks cube or take it apart and put it back together?
posted by smcniven at 6:26 PM on March 22, 2005