Question 60
Suppose a magician can perform each of the following 3 kinds of tricks any number of times:
* Trick A: Change 1 orange and 1 grape into 2 apples.
* Trick B: Change 1 grape and 1 apple into 3 oranges
* Trick C: Change 1 apple and 1 orange into 4 grapes.
Initially, there were 2011 each of apples, grapes and oranges, and the magician performed a number of tricks and ended up with the situation in which there are 2011 apples, 2011 grapes and more than 2011 oranges. What is the smallest possible number of oranges in this situation?
* Trick A: Change 1 orange and 1 grape into 2 apples.
* Trick B: Change 1 grape and 1 apple into 3 oranges
* Trick C: Change 1 apple and 1 orange into 4 grapes.
Initially, there were 2011 each of apples, grapes and oranges, and the magician performed a number of tricks and ended up with the situation in which there are 2011 apples, 2011 grapes and more than 2011 oranges. What is the smallest possible number of oranges in this situation?