### Favorite puzzles

I'm going to start posting some of my favorite puzzles.

Puzzle 1:

Let's say you have a cup of cream and a cup of coffee (same volume). You take a spoon full of cream and mix it in with the coffee. Now, you take a spoon full of the mixed coffee/cream and and mix it with the cream. Is there more coffee in the cream cup or is there more cream in the coffee cup?

Puzzle 1:

Let's say you have a cup of cream and a cup of coffee (same volume). You take a spoon full of cream and mix it in with the coffee. Now, you take a spoon full of the mixed coffee/cream and and mix it with the cream. Is there more coffee in the cream cup or is there more cream in the coffee cup?

## 6 Comments:

more cream in the cream cup?

wouldn't they be equal?

the act of mixing the coffee/cream together means that a spoonful of the mixture back into the cream will only return a fraction of that original cream volume. If one assumes that the mix dispersed the cream evenly throughout the coffee, there'd be way more coffee than cream in that spoonful... probably around the same amount of cream that's now dispersed throughout the coffee cup.

this is of course barring any sort of weird dispersion effects because of differences in the material properties of the liquids that I'm unaware of :)

I think they'd be equal too.

Yup same amount. Assume the you start with 40 parts of Cream(X) and 40 parts of Coffee(Y).

And assume that the spoon transfers 10 parts of the liquid. Yes, it's a huge spoon. :)

40X and 40Y

Transfer 10X

30X and 40Y + 10X

Transfer 10 Part i.e 1/5 of 40Y + 10X

i.e. Transfer 8Y + 2X

32X + 8Y and 32Y + 8X

Hmm, I remember something about liquid in liquid solution and that the total volume of X in Y will be less than X+Y. I thought that's the point of the question assuming that spoon size is much smaller than the size of the cup. So I assumed 10 Parts of 40Y+10X is 1/4 not 1/5:

(40X,40Y)

(30X,40Y+10X)

(31X+10Y,30Y,9X)

looks preatty difficult

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