12

Part of 2000 Harvard-MIT Mathematics Tournament

Problems(2)

2000 Guts #12: Choosing 2 consecutive numbers

Source:

Calculate the number of ways of choosing

4

numbers from the set

{1,2,\cdots ,11}

such that at least

2

of the numbers are consecutive.

2000 HMMT RMT Team #12

Source:

At a dance, Abhinav starts from point

(a, 0)

and moves along the negative

x

direction with speed

v_a

, while Pei-Hsin starts from

(0,6)

and glides in the negative

y

-direction with speed

v_b

. What is the distance of closest approach between the two?

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