The following is a variant of a problem that appeared on a college entrance examination. In the figure below, the radius of circle A is 2 units, the radius of circle B is 3 units. Starting from the position shown in the figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle A first reach its starting point?
Diophantus, the Greek mathematician known as the "Father of Algebra", supposedly had the following inscribed on his tombstone:
"Diophantus passed 1/6th of his life in childhood, 1/12th in youth, and 1/7th more as a bachelor.
Five years after his marriage, there was born a son who died four years before his father, at half his father's age."
How old was Diophantus when he died?
You are visiting your girlfriend and she orders pizza. Your evil girlfriend has perfect eyesight and notices fly droppings in three places on the pizza. She is seeking revenge on you for refusing to babysit her poodle and proceeds to cut the pizza. Assuming that the droppings occurred independently and in random places, what is the probability (the solution format is x/y where gcd(x,y) = 1) that she will be able to cut a half-circle pizza slice with all three droppings in one half?
A meatball has four fly droppings on it. These droppings, are in random places and you must calculate the probability (x/y format, gcd(x,y)=1) that you are able to cut a semi-sphere with all four droppings on one side.
The University is considering issuing new student ID cards (again!). Each student will be assigned a 5 digit identification number from 00000 to 99999. For ease in record keeping, the registrar has requested that any two ID numbers differ in at least two places. How many ID's could the registrar issue?
if you look at my explanation is pretty much your formula for n between 3 and 4
500(1 + 1/3 + 1/5 + k/7) = 800, where k = n - 3
Another cool thing i noticed looking at your formula is that you just proof that the series is divergent, and with the common constrains any desert can be crossed (of course n grows exponentially).
Lets assume that your solution is the right one, and indeed with 3.44 loads we can cross 800 miles:
with 1 load , we can go 500 miles
with 2 loads , we can go 500(1+1/3) = 666.66
with 3 loads, 500(1+1/3+1/5) = 766.66
now, it means that 3.44 - 3 = 0.44 loads we can get (800 - 766.66)x7 (we need 7 trips now to make a cache of 3 loads)
0.44 x 500miles/load = 220miles , (800 - 766.66)x7 = 233.38
0.4666 x 500miles/load = 233.3 (much closer to the answer)
An unlimited supply of gasoline is available at one edge of a desert 800 miles wide, but there is no source in the desert itself. A truck can carry enough gasoline to go 500 miles (this is called the "load"), and it can build its own refueling stations at any spot along the way.
What is the minimum amount of gasoline (in loads) the truck will require in order to cross the desert?