# statistics – How to spread N numbers evenly across K containers?

## Question:

I can't figure out how this problem is optimally solved:

There is a "random" set of N numbers from 0 to M. The distribution is approximately exponential: there are more small ones.

They should be scattered among K containers so as to minimize the spread of the sums of numbers in the containers .

I thought it was necessary to find an average to strive for; sort the set and take from the edges. But it is not clear where to stop when I collect the amount in the next container. So, I missed the "golden mean" 5%, is that good, or still try? Obviously, it is not optimal to take it at random.

Upd. probably not the easiest task. It looks like a one-dimensional " packing problem " + combinatorics.

Which immediately comes to mind (but he doesn't seem to be that good).
Start spreading with large numbers and scattering into the smallest cell. Smaller values ​​will trim inequality.

Update

I don't understand why it is hard to take the largest + the smallest? We sort in descending order, for example, we got `[5 4 3 3 2 2 1 1 1]` . And you need to split it into 3 containers:

1. 5 = 4 = 3 // took the 3 largest: 5,4,3
2. 5 = 4 = 6 // number 3
3. 5 = 6 = 6 // number 2
4. 7 = 6 = 6 // number 2
5. 7 = 7 = 7 // two numbers 1, 1
6. 8 = 7 = 7 // last number 1

I consider this method to be the simplest, but, unfortunately, there are cases when the spread will be imperfect.

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