How Many Candies In The Jar?
 

First day of school. My son's 6th grade teacher has a clear, sealed jar of Jolly Ranchers on her desk. The kid who comes closest to the correct number of candies, wins the jar and contents. Please recommend approaches to win this. I have given him a couple but I may be overlooking the obvious.

6th grade? I guess the teachers goal is to have them figure volume of a cylinder and estimating? Can they measure the jar or do they have to estimate that as well?

Buy a jar the same size and fill it with the same. I guess that would be cheating ;-{

I think it is usually just look at it, no measuring devices.

If your kid can talk you into that, I think he's pretty clever.

That way, he doesn't have to win (or even bother entering) the contest to get the jar and the candy.

That kid would have a bright future in arbitrage.

My son suggesting weighing.

Volume calculation, and some experimental estimation of the airspace, was another approach.

I thought maybe one could count the number of candies visible in the bottom layer.

The goal is not to buy the equivalent number of candies. I'm going to make him share them with the class anyway. No way I want him chowing down on 100s of Jolly Ranchers.

I believe she is going to collect suggested methods and have the class see what works, rather than simply announce a winner.

If not that, have him put a ruler across the base and height and take a cell phone pic and do a volume calculation pi x r^2 x H and do a volume calc on one candy (IIRC pi x r^3) and go from there. Estimate void space.

Go back at night, open jar, count candy, close. Give correct answer in the morning....

Yes, but it needs a real world 'educational element'. I would suggest elements of basic electronics (defeating the alarm), manual dexterity (lock picking), or every day real world commerce (just bribe the janitor).

You haven't provided enough data.
He needs to ask if there is anything inside the jar besides candy and air. She may have hid a filler in the center to throw off measurements.
Will she let him measure the jar, weigh the jar, or pick up the jar? If the answer is no to all of these, then put something next to the jar that you can measure and observe or photo the two objects from two planes to get an idea of the approximate size. From there he can estimate how many candies per layer and how many layers to get a rough number or, do a volume calculation but the air space makes it a little complex. If he can weigh the jar he'll find a way to know the weight of the jar empty.

Don't mess around, go back at night and steal the freaking jar.

Count the bottom layer through the glass, and multiply by the height.

Most accurate is weighing a clone of the jar and then weighing jolly ranchers. Electronics manufacturers run inventory by weight. Very accurate.

Another idea is to check if the jar is partially full. If so, find a number of jolly rancher packages that will approximately fill to the same volume and count. This approach assumes that the filler will fill to the supply rather than fill to the jar.

Sounds fun!
Larry

We could really have fun with this one but it would go straight to PARF (aka Hell).
Was the word "suite" (used instead of suit) a pun for sweet?

Arbitrage? Did you mean arbitration?

You need Dustin Hoffman to take a look at it ...

a: calculate volume of jar from dimensions.
b: calculate volume of a candy from dimensions.

c: a/b then subtract 30% (ish).

d. submit guess.

d. bring teacher $100 for discretionary spending on "educational materials."

e. collect prize.

f. run for congress.

the answer is obviously 42

No, arbitrage. The art of guaranteed profit/return with little/no risk.

There are some really funny people in this forum! I used to win stuff like this all the time using dad911's suggestion. I learned it being on the math team. Yes, I was that big of a nerd in school. Problem is that a lot of these contest things don't let you pick up the jar and count the objects in a "layer" because they caught on to people like me. But for a while there, I got pretty good at it and whenever I saw a contest like that, I would do it.