The Jellybean Winner!

Posted November 22nd, 2012

Huge congratulations to Barbara Fontana who guessed the exact number of jellybeans in the jar - 735!

Bryony Dyer and Barnaby Gregory were very close behind though, both guessing 737! Thanks to all who got involved, we love doing these little competitions and the hundreds of e-mail responses we receive just make us laugh! We thought we would share the most impressive response we got with you. This is from Bailey F, who was only off-bean by 9!

"As a scientist, I'm going to need to work through this in a logical way showing all my working. My answer's at the bottom.

First of all, I'm immediately going to take 1cm off the circumference to account for the thickness of the glass (the inner circmference will always be a bit less than the outer circumference. I'll also take a bit off the height to account for the lid, the thickness of the glass at the bottom of the jar, and the bit of empty space at the top. Let's go with 16cm.

So new assumptions: 35cm circumference, 16cm height

Volume of a cylinder = pi(r^2) * h

r = (35/pi)/2 = 5.57

so, volume of jar = pi * 5.57 * 5.57 * 16 = 1558 cm^3

Now we need to figure out the volume of a jelly bean. As a rough measurement, I'll say it's a cylinder with radius 0.5 cm and length 2 cm.

So, volume of jelly bean = pi * 0.5 *0.5 * 2 = 1.57 cm^3

The maximum number of jelly beans that the jar could fit would therefore be 1558/1.57 = 992

However, there will be a certain amount of empty space between the jelly beans that needs to be accounted for. I'd take off another 20% but I also haven't accounted for the tapering at the top of the jar so let's go for 25%. 0.75 * 992 = 744

Therefore there are 744 jelly beans in the jar."