Discrete Mathematics Warmups
What is the probability (to 3 decimal places) that a point \(P\) picked uniformly at random inside an equilateral triangle, is closer to the centroid than to its sides?
by
Sharky Kesa
Consider the set \( \mathbb{S} =\{B,R,I,L,A,N,T\}\). How many ways are there for us to partition the set into any number of non empty disjoint subsets whose Union is \(\mathbb{S} \)?.
by
Shubhendra Singh
Suppose two real numbers \(x\) and \(y\) are chosen, uniformly and at random, from the open interval \((0,1)\). Let \(P\) be the probability that the integer closest to \(\dfrac{x}{y}\) is odd.
Find \(\lceil 10000P \rceil\).
by
Brian Charlesworth
Let \(a_0, a_1, \cdots, a_7\) be any \(8\) distinct integers. Let \(P\) be the product of their pairwise differences, that is:
\[P = \prod _ {i < j} {(a_i - a_j)} \]
What is the greatest integer which always divides \(P?\)
by
Agnishom Chattopadhyay
In the above image, how many rectangles are there which do not include any red squares?
by
Chung Kevin