2

Part of 2017 BMT Spring

Problems(5)

BMT 2017 Spring - Geometry 2

Source:

S

be the set of points

A

in the xy-plane such that the four points

A

(2, 3)

(-1, 0)

(0, 6)

form the vertices of a parallelogram. Let

P

be the convex polygon whose vertices are the points in

S

. What is the area of

P

2017 BMT Team 2

Source:

900

Choco Pies. He realizes that for some integer values of

n \le 900

, if he eats n pies a day, he will be able to eat the same number of pies every day until he runs out. How many possible values of

n

algebranumber theory

equilateral and square of equal perimeter 2017 BMT Individual 2

Source:

Barack is an equilateral triangle and Michelle is a square. If Barack and Michelle each have perimeter

12

, find the area of the polygon with larger area.

geometryperimeterareasEquilateralsquare

2017 BMT Discrete #2

Source:

Each BMT, every student chooses one of three focus rounds to take. Bob plans to attend BMT for the next

4

years and wants to gure out what focus round to take each year. Given that he wants to take each focus round at least once, how many ways can he choose which round to take each year?

2017 BMT Analysis #2

Source:

Find all solutions to

3^x-9^{x-1} = 2.