Answer the following questions by applying the pigeonhole principle. For each blank, write in the number in numeral form. For example, if the answer is ten, simply write 10. a) What is the minimum number of integers that you must pick between 0 and 9 (inclusive), such that two of them add up to 9?

b) In a class of 30 students, each student can pick between 10 different home-works. What is the minimum number of students needed to ensure that two students get the same home-work?

c) I have 9 pairs of socks of different colors in a box. How many must I grab to ensure that I'll have at least one matching set?

d) I also have 9 sets of gloves of different colors in the same box. How many different objects must I grab to ensure that I have one matching set of gloves or socks?

e) What is the minimum number of rooks from a chess game that we must place on an 7X7 grid, such that at least two of them threaten each other?