A6/B8

Part of 2008 Princeton University Math Competition

Problems(2)

2008 PUMaC Combinatorics A6 / B8

Source:

xxxx

xx

x

x

In how many ways can you fill in the

x

s with the numbers

1-8

so that for each

x

, the numbers below and to the right are higher.

2008 PUMaC Number Theory A6 / B8

Source:

What is the largest integer which cannot be expressed as

2008x + 2009y + 2010z

for some positive integers

x, y

z