I found a maths puzzle somewhere and a part of it as below:
Kelly wants to place n objects $a_1,a_2,⋅⋅⋅,a_n$ into two bags. For each $i=1,2,⋅⋅⋅,n$, the weight of $a_i$ is $w_i$ kilograms.
The capacity of each bag is not a problem as it is not limited.
Kelly wants to minimize the weight of the most heavy bag. So this is what she does:
She ordered in an arbitrary order. She always places the object under consideration into the least heavy bag.
At the end when all objects are in the bags, Kelly finds that the weight of the most heavy bag is at most 3/2 times the optimum.
How? ? ? How can she get to know that?
Extended version of Weights - Objects into bags puzzle.
Any examples would make me understand better.Can we deduce a formula for such cases?