Hello, Obsidantion!

There are two cups of different liquids. Both liquids are equal in volume.

If I take a teaspoon of one liquid and put it in the other,

then mix that until the entire liquid is equally concentrated,

then take a teaspoon of that cups mixture and put it in the first cup,

which cup has a greater concentration of its original liquid and why? This is a classic (very old) problem.

We have equal amounts of the two liquids, O's and X's. Code:

| | | |
| | | |
| | | |
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
*-----* *-----*
A B

A specific amount is tranferred from A to B. Code:

| | | |
| | |OOOOO|
| | |OOOOO|
| | |XXXXX|
| | |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
*-----* *-----*
A B

The combination is thoroughly mixed.

Code:

| | | |
| | |OXOXO|
| | |XOXOX|
| | |XXXXX|
| | |XXXOX|
|OOOOO| |OXOXX|
|OOOOO| |XOXXX|
|OOOOO| |XXOXX|
*-----* *-----*
A B

The same amount is transferred from B to A.

Code:

| | | |
| | | |
| | | |
|OXOXO| |XXXXX|
|XOXOX| |XXXOX|
|OOOOO| |OXOXX|
|OOOOO| |XOXXX|
|OOOOO| |XXOXX|
*-----* *-----*
A B

If we let the liquids "separate", we see the obvious. Code:

| | | |
| | | |
| | | |
|XXXXX| |OOOOO|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
|OOOOO| |XXXXX|
*-----* *-----*
A B

The amount of X's in cup A must be **equal to** the amount of O's in cup B.

__Neither__ cup has a greater concentration of its original liquid.