Ah, fall! There are some leaves on a tree. They are red, orange, yellow, or green, and possibly, more than one of the colours.
There are 500 red leaves, 1500 orange leaves, 2000 yellow leaves, and 2000 green leaves.
Given that 1) all red leaves are also orange, 2) one-half of the yellow leaves are also green, and 3) one-half of the orange leaves are also yellow, answer the following:
- What is the maximum number of leaves possible? The minimum?
- What is the maximum number of leaf colour combinations possible? The minimum?
- Is it possible for there to be a leaf that is all four colours?
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, November 13, 2013 at noon Pacific Time. I will post the answer shortly after.