A4 / B6

Part of 2011 Princeton University Math Competition

Problems(2)

2011 PUMaC Combinatorics A4 / B6

Source:

N

be the number of ways to place

4

5 \times 5

chessboard such that no

3

are on the same diagonal. Find the remainder when

N

100

. (Note: the length of a diagonal on a

5 \times 5

chessboard can be 2, 3, 4, or 5.)

2011 PUMaC Number Theory A4 / B6

Source:

For how many ordered triplets of three positive integers is it true that their product is four more than twice their sum?