Dear Dr Maths
At a recent fundraising event I attended there was an activity to guess the number of sweets in the jar. Is there a mathematical way to improve your chance of being correct?
Sarah, Newcastle
An approximate method to calculate the number of sweets in a jar, is to multiply the number along the width and length of the base by the number of sweets in the height of the jar.
Granular Matter theory then tells us that on average a jar of mixed shapes will have about a 30% air gap in between the sweets. This percentage value will of course vary depending on the shape of the sweet. For example, an unshaken jar of spherical shaped sweets will have a gap of 39%, but if you gently shake them a few times this will drop to 35%.
For a jar with 6 sweets along both the width and length of the base and a depth of 15 sweets you would need to calculate 6x6x15=540. Then to take account of the gap in between the sweets, reduce this total by thirty percent 0.70×540 giving an answer of 378 sweets in the jar.
Here is a puzzle for you to try:
If a jar has approximately 4 sweets along the width, 5 along the length and a depth of 12 sweets, how many sweets are in the jar?
210
210
168
240
240
168 because after getting 240 you have to multiply by .70 to account for the gap.
168
168 is the same answer I calculated
4×5×12=240
240-30%=168
Wouldn’t this assume the jar is square?
This would mean that there are right angles, along the front would be 6 lollies across while the sides will be 6 across, this would add corners, would you have to subtract (4×15) to remove the corners and round it out a little more
Just multiply the height and the amount of candy touching the entire bottom