When we need to use the Pigeonhole theorem and why we are using the Pigeonhole theorem in this case?
I also have a question below:
Each tile has one letter on it, and a point value in the bottom right hand corner (e.g. "M" is worth 3 points). $$M_3A_1T_1H_4E_1M_3A_1T_1I_1C_3S_1$$
Suppose that the pictured tiles get split between two bags. Which of the following statements follows from the pigeonhole principle?
a)Both bags will contain at least 3 tiles worth 1 point.
b)One bag will contain at least 4 tiles worth 1 point, the other bag will have at most 3 tiles worth 1 point.
c)One bag will have more points on its tiles than the other bag.
d)Both bags must contain a tile with the letter M on it.
e)Both bags will have the same number of tiles in them.
I am thinking b) might be the answer but I am just guessing based on my logic and nothing about the Pigeonhole theorem. I know d) and e) must be wrong as 2Ms can be put in one bag and there is 11 elements, it is impossible to have the same number of tiles in two bags.
Please correct me if I am wrong