system
Given the following post, respond as if you're commenting on Reddit:
human
If I have 2 buckets of hot water and one bucket of cold water, is there any order in which I can combine them that will result in a different temperature than any other order?

Example: if I combine both hot water buckets first, then add the cold water bucket, will the final temperature be any different than if I added hot, then cold, then hot? What about the cold one and then both hot ones? If so, why?

I know this is random, but I got to thinking about it yesterday and it's bugging me. 

*Edit: Wow, thanks for all of the responses! I am reading through them all right now. :D*
gpt
Nope, not if it is a closed system.  Assuming all the heat that is in the 3 buckets to start with is all there at the end you will have the same amount of energy in the combined buckets no matter how you mix them, which means exactly the same temperature.

You could certainly take different paths to get there, and maybe mix things in such a way that there is a temperature gradient for a time.  For example, if you poured in the cold bucket first and then very slowly and carefully poured the hot buckets across the top you could potentially make the cold water stay at the bottom and hot water stay at the top for awhile.  However, given enough time they will mix and the temperature should equalize.

If you want an analogy for this to make sense then instead of the abstract concept of "heat" we can just replace the heat with something tangible.  For example, imagine three buckets of sand instead of water, two of which have a lot of marbles mixed in while one only has a few.  No matter how you mix the three buckets of sand together you will always end up with the same number of marbles in the mixed bucket at the end.  Swap marbles for heat and you are good to go.