Thread: Calculating Amount of Candies in a Jar

I know there are many variables based on size of each candy, etc, but is there anyone who knows an accurate(ish) method for calculating how many candies are in a jar?


thanks

Do try measuring the volume of one candy and measuring the volume of the bottle. Of course, there is space between candies, but I think it's the most accurate method you can get.

If they are spherical candies you could use the random close packing density to estimate it.
http://en.wikipedia.org/wiki/Random_close_pack

I would weigh the jar, subtract the weight of the empty jar, and divide that by the average weight of a piece of candy.

Volume of jar > volume of sum of candies in jar. Since the jar is continuous and the candies are discrete than it's impossible for the number of candies in the jar to equal the jar itself. If the jar is filled with candies than you can divide the number of candies in the jar by the volume of a single candy in order to get a fairly accurate estimation, but it will be somewhat greater than the actual answer.

Originally Posted by Ellatha

Volume of jar > volume of sum of candies in jar. Since the jar is continuous and the candies are discrete than it's impossible for the number of candies in the jar to equal the jar itself. If the jar is filled with candies than you can divide the number of candies in the jar by the volume of a single candy in order to get a fairly accurate estimation, but it will be somewhat greater than the actual answer.

I realize this should work, yet my problem is that there are many types of candy in the jar. These candies vary in size and there is nothing saying that there are the same amount of each type of candy in the jar.

Originally Posted by Pomegranate Luke

Originally Posted by Ellatha

Volume of jar > volume of sum of candies in jar. Since the jar is continuous and the candies are discrete than it's impossible for the number of candies in the jar to equal the jar itself. If the jar is filled with candies than you can divide the number of candies in the jar by the volume of a single candy in order to get a fairly accurate estimation, but it will be somewhat greater than the actual answer.

I realize this should work, yet my problem is that there are many types of candy in the jar. These candies vary in size and there is nothing saying that there are the same amount of each type of candy in the jar.

If there is more than one type of candy in a jar than it's impossible with a reasonable estimate without simply counting them.

This is, indeed, my predicament. However, I am trying to find some way to reasonably estimate the amount of candy there is. It seems as though this is impossible, though, but thank you for you help.

So is it fair to assume you're trying to win a contest or something? And you are not allowed to weigh the jar and experiment with it? Because otherwise, using the weight as I mentioned above really is a pretty good method.... :?

I may have a solution for you, but it is predicated upon a couple of assumptions which may or may not be true.

Assumption 1. See through jar.
Assumption 2. Random distribution of the candies in the jar.
Assumption 3. The volume and weight of the jar can be known.
Assumption 4. The volume and weight of each kind of candy can be known.

First count how many of each type are able to be seen to approximate the ratios of the different candies.

Determine the total weight of the candies.

Determine the volume of the empty space in the jar by pouring sand in to fill the empty spaces and subtract the volume of sand used from the jar volume for the volume of the candy. (or use water if preserving the candy isn't required)

Determine volume and weight of each type of candy.

You should then be able to use the ratios, volume and weight to construct a sufficient number of linear equations; just solve the system and you're done.

If the jar is transparent, you may be on the brink of your first adventure in stereology.

Warning: deriving the formula, if at all possible in your context, will take much more effort than actually counting the candies. But it may be worth it if you are to assess the number of candies in jars for 8 hours a day for the next decade (my condolences). And if you are doing this for a science contest, a firmly grounded stereological approach is guaranteed to impress the jury.