1

Part of 2017 BMT Spring

Problems(5)

BMT 2017 Spring - Geometry 1

Source:

What is the largest

n

such that there exists a non-degenerate convex

n

-gon such that each of its angles are an integer number of degrees, and are all distinct?

2017 BMT Team 1

Source:

You are racing an Artificially Intelligent Robot, called Al, that you built. You can run at a constant speed of

10

m/s throughout the race. Meanwhile, Al starts running at a constant speed of

1

m/s. Thereafter, when exactly

1

second has passed from when Al last changed its speed, Al’s speed instantaneously becomes

1

m/s faster, so that Al runs at a constant speed of

k

m/s in the kth second of the race. (Start counting seconds at

1

). Suppose Al beats you by exactly

1

second. How many meters was the race?

2017 BMT Individual 1

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In three years, Xingyou’s age in years will be twice his current height in feet. If Xingyou’s current age in years is also his current height in feet, what is Xingyou’s age in years right now?

2017 BMT Discrete #1

Source:

9

colors of socks and

5

socks of each type of color. Pick two socks randomly. What is the probability that they are the same color?

2017 BMT Analysis #1

Source:

10

students take the Analysis Round. The average score was a

3

and the high score was a

7

. If no one got a

0

, what is the maximum number of students that could have achieved the high score?