12
Part of 2008 AIME Problems
Problems(2)
Cars on Highway
Source: 2008 AIME I Problem 12
3/23/2008
On a long straight stretch of one-way single-lane highway, cars all travel at the same speed and all obey the safety rule: the distance from the back of the car ahead to the front of the car behind is exactly one car length for each 15 kilometers per hour of speed or fraction thereof (Thus the front of a car traveling 52 kilometers per hour will be four car lengths behind the back of the car in front of it.) A photoelectric eye by the side of the road counts the number of cars that pass in one hour. Assuming that each car is 4 meters long and that the cars can travel at any speed, let be the maximum whole number of cars that can pass the photoelectric eye in one hour. Find the quotient when is divided by 10.
calculuslimitAsymptotefunctionAMC
Blue/Green Flags
Source: AIME 2008II Problem 12
4/3/2008
There are two distinguishable flagpoles, and there are flags, of which are identical blue flags, and are identical green flags. Let be the number of distinguishable arrangements using all of the flags in which each flagpole has at least one flag and no two green flags on either pole are adjacent. Find the remainder when is divided by .
countingdistinguishabilityAMC