I always have trouble trying to exactly identifying the exact pigeon and the pigeonholes for questions with slightly more integers. For example, questions like this.
Eleven integer are chosen from 1 to 20 inclusive. Use pigeonhole principle to prove the selection include integer a and b such that b = a + 1
To me, it's a little confusing because of the number of integers and the integer a and b.
Is it safe for me to assume the
pigeon = 2 because of the integer a and b while the
pigeonhole = 11 because of the chosen eleven integer?
The above seems to be less confusing compared to another question that uses
A fruit basket that contains 10 apples, 8 oranges and 9 banana. If someone pick some fruits without looking, use the generalized pigeonhole principle to determine how many must you pick to be sure of getting at least 5 fruits of the same type
With so many potential values lingering in the question, is there any way to simply and identify the
pigeonhole to use the
generalized pigeonhole to prove it?