There are 2011 distinct points on a circle. If you connect two of them to form a line and then connect a different two to form another line, what is the probability that the two lines intersect inside the circle?
Let H and T be the end points of a line 1 unit long. Starting at the centre, flip a coin. If it’s heads then move half way betwen the current position and H. If it’s tails then move half way betwen the current position and T.
On average, how far from the centre will you [...]
How many ways can you make $2010 dollars, using only $2, $5 and $10 notes?
e.g. 5 *$2 + 2*$5 + 1990*$10 or 201*$10.
Find the number of positive integer solutions to n^x + n^y = n^z with n^z < 2011.
Uniformly randomly choose three integers in the range 1 to 15. What is the probability that the sum is divisible by 3 if you replace the numbers, and if you don’t replace the numbers?
For consistency use C(n,r) = n!/((n-r)! r!) and P(n,r) = n!/(n-r)! for the combinations and permutations functions.
(As usual, it’s this or [...]