I have a question regarding the Pigeonhole Principal. I essentially understand what it is but I am stuck on a problem:

18 pennies are placed on the squares of a 6x6 chess board randomly, up to one penny on each square of the 36. 

a) Prove that there is a row and column of the board that contain at least 5 pennies together. 

b) Show that there is an arrangement of the 18 pennies in a way such that no row-column combination would contain more than 6 pennies.

How would I go about this problem? I just can't seem to grasp the concept 100% especially one that would involve some drawings. Thank you.