Stingers

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Math Stinger #152

This is a test.

 

Math Stinger #151 
Going at top speed, Grand Prix driver x leads his rival y by a steady three miles.  Only two miles from the finish, x runs out of fuel.  Thereafter x's deceleration is proportional to the square of his remaining velocity, and, in the next mile, his speed exactly halves.  Who wins, and why?
Please send solutions to tchan4 at kennesaw dot edu.

 

Math Stinger #150
Let us assume that a given pair of people either know each other or are strangers.  If six people enter a room, show that there must be either three people who know each other pairwise or three people who are pairwise strangers. 
Please send solutions to tchan4 at kennesaw dot edu.

Math Stinger #148
For two given positive integers n and k, how many different sequences of positive integers a1 ≤ a2 ≤ a3 ≤ ... ≤ ak are there in which ak ≤ n?
Please send solutions to tchan4 at kennesaw dot edu.

 

Older solutions published to: Solved Stingers