What is the probability (to 3 decimal places) that a point picked uniformly at random inside an equilateral triangle, is closer to the centroid than to its sides?
Consider the set . How many ways are there for us to partition the set into any number of non empty disjoint subsets whose Union is ?.
Suppose two real numbers and are chosen, uniformly and at random, from the open interval . Let be the probability that the integer closest to is odd.
Find .
Let be any distinct integers. Let be the product of their pairwise differences, that is:
What is the greatest integer which always divides
In the above image, how many rectangles are there which do not include any red squares?