A1 / B2

Part of 2011 Princeton University Math Competition

Problems(2)

2011 PUMaC Combinatorics A1 / B2

Source:

Consider the sum

\overline{a b} + \overline{ c d e}

, where each of the letters is a distinct digit between

1

5

. How many values are possible for this sum?

2011 PUMaC Geometry A1 / B2

Source:

Two logs of length 10 are laying on the ground touching each other. Their radii are 3 and 1, and the smaller log is fastened to the ground. The bigger log rolls over the smaller log without slipping, and stops as soon as it touches the ground again. The volume of the set of points swept out by the larger log as it rolls over the smaller one can be expressed as

n \pi

n

is an integer. Find

n