# Jelly Bean Guess

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Calculator / Last modified by AndrewBudd on 2018/08/20 14:52
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The Candies in a Jar calculator computes the number of candies in a jar, bowl or other container (estimated).   This is useful in the "Count the Candies" contest seen around the world.  It uses the volume density of the candies and the calculated estimate volume of different shape of containers to provide a good estimate of the number of candies in the container.  See YouTube video instructions HERE.

INSTRUCTIONS:

1. Container Shape: Identify the shape of the container and click on the calculator button that corresponds to that shape.
2. Container Size: Enter your best estimate for the dimensions of the candies in container.  Note: people are much better a estimating one dimension (height, length, width) than volume, so give it a shot.
3. Type of Candy: Choose the kind of candy that's in the container from the list.  The default candy is regular jelly beans.  However, highly scientific (and delicious) measurements have also been made for mini jelly beans, regular jelly beans, jumbo jelly beans, M&Ms, Peanut M&Ms and gum balls.

How many Candies: The calculator returns an estimate on the number of candies in the container.

For more information on Jelly Beans, click HERE for a fun article from The Celebrity Cafe.

#### Container Shapes

What is the shape of the candy container?  This calculator uses five container shapes and gives you a formula based on each of the shapes.

1. Cylindrical -  This is the straight up and down jar with the round opening at the top.  You need the diameter of the top (d) and the height (h) of the candies in the jar.
2. Rectangular - This is a straight up and down squared-off container (e.g. cardboard milk carton).  You need the base measurements (d and w) and height (h) of the candies in the jar.
3. Spherical  -  This is a round, globe like, container.  You need the diameter (d) of the container in the middle (broadest) part of the bowl, and the the height (h) of the candies in the jar.
4. Tapered rectangular - This is the bowl with a squared bottom and a squared top, but not straight up and down.  The sides of the top are bigger or smaller than the sides of the bottom. Again, no worries.  Provide the length of a single side of the top (b) and the length of a single side of the bottom (B), and the height (h) of the candies in the jar.
5. Tapered Round - This is a bowl with a round bottom and a round top, but not straight up and down.  The rounded top is bigger or smaller than the bottom.  No worries.  Provide the diameter of the top (B) and the diameter of the bottom (b) and the height (h) of the candies in the jar.
6. Quart Mason Jar -  This computes how many candies are in a standard quart mason jar.
7. Curved Bowl - This is a common curved round bowl with a width (W) and depth (D).
8. Irregular shape - This one requires you to guess on the volume of the jelly beans in the container.  Try to imagine how many liters or cups or pints or quarts or gallons it would take to fill the container to the level of the candies.  Enter that volume (v) and make sure you pick your units (e.g. liters, pints, gallons).
Quart Mason Jar          Cylindrical Jar
Good luck!  If you win, give vCalc a shout out on social media and give a bit of your winnings to charity.

### The math

The math behind these formulas are pretty straight forward.  We use basic euclidean (3D) geometry to compute the volume of the shapes. The geometric names of the shapes are

• cylinder
• rectangular parallelepiped.  Isn't that a terrible name for a box?
• sphere
• frustum of a pyramid.
• frustum of a cone
• paraboloid.  That's a terrible name for a bowl!

Frustum is just a slice of an object were the top and bottom slices are parallel.

Once we know the volume, we are able to make our guess based on an average number of candies in a known volume.

We bought large bags of the different types of candies and measured them in kitchen measuring bowls.  Then we counted the number of candies and did the math to get the estimated number of candies in a a gallon container.  Here the results:

• Mini Jelly Beans: 3,500 mini Jelly Bean candies in a gallon.
• Jelly Beans:  930 Jelly Beans in a gallon
• Jumbo Jelly Beans: 736 Jumbo sized Jelly Beans in a gallon
• M&Ms:  3991 plain M&Ms in a gallon.
• Peanut M&Ms: 1248 Peanut M&Ms in a gallon
• Gum Balls: 1264 Gum Balls in a gallon.

This is only an estimate, because the candy manufactures may vary the sizes of the candies, but this is a decent estimate of the average size of the different candies and your guess, using these calculators, will be much less of a  guess.

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