I was looking at this problem on Puzzle StackExchange about working out the proportion of sand in two separate beakers. Rather than providing a mathematical explanation, I thought it would be easiest to try and illustrate this visually, but I would like to know what the mathematical solution would be for any given size of beakers and cups. I was hoping that someone would be able to explain this relationship a little bit better, and I can come up with a diagram that will help illustrate this problem better.
The problem is also summarized here:
You have two large beakers of the same size.
- Beaker A is half filled with blue sand.
- Beaker B is half filled with red sand.
Steps:
- You take a cup of blue sand from Beaker A and pour it into Beaker B.
- You mix up the contents of Beaker B until the colour is consistent.
- You take a cup of the contents of Beaker B and pour it into A.
- You mix up the contents of Beaker A until the colour is consistent.
Which is there now more of:
- Blue sand in Beaker B or
- Red sand in Beaker A?
The total amount of sand in each beaker is the same at the end as it was at the beginning. So, whatever amount of blue sand is missing from A has left a space which must have been filled by an equal amount of red.
Therefore, the amount of blue in B at the end is the same as the amount of red in A.