Understand the problem Two subsets of the set are to be chosen so that their union is and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter? Source of the...

Understand the problem A group of pirates agree to divide a treasure chest of gold coins among themselves as follows. The pirate to take a share takes of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which...

Understand the problem A sequence of natural numbers is constructed by listing the first , then skipping one, listing the next , skipping , listing , skipping , and, on the th iteration, listing and skipping . The sequence begins . What is the th number in the...

Understand the problem Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will...

Understand the problem For some positive integer , the number has positive integer divisors, including and the number . How many positive integer divisors does the number have ? Source of the problem American Mathematics Competition Topic Number Theory...