Eggciting work puzzle: Eggs in a Jar

Hey folks,

We have an interesting puzzle floating around the office.  We were asked to guess how many chocolate eggs there were in a jar.  This jar has gone around the offices and people have been guessing ... but I thought that there has to be an easier way using an optimal packing problem.

My assumptions are that eggs can be approximated to be spheres.  If we can estimate the average radius and the imnner dimentions of the jar then we could give and estimate.

N ≤ (π / (3√2)) (Vc/Vs)

ie: N ≤ 0.74048(Vc/Vs)

where Vc cylinder volume and Vs sphere (egg) volume

N is the final best approximation - walls add in loss depending

What my Customer Service Manager measured

Diameter of bottom of jar = 110mm 

Diameter of top of jar = 85mm 

Jar height: 

= 140 mm (up until it starts to change shape and curve inwards) 

= 15 mm (from the curve to the lid) 

Large egg: 

= 30mm height = 22mm wide + deep 

 Small egg: = 22mm high 

= 17 mm wide + deep 

Taking a average of egg size of 22.75mm diameter and packing them in optimalthe constant ly to the extent of the volume we get a max of 169 optimised and 146 sub optimised

Interested if you have a differing answer to this EGGciting conundrome.

_{*More fun background reading here https://math.stackexchange.com/questions/4079254/how-many-spheres-can-fit-inside-a-cylinder-container}