Problem solving is defined as the process of finding solutions to difficult or complex issues. At its very core, math is the essence of problem solving. When studying mathematics, issues arise that are often complex in nature, and formulas and mathematical algorithms are used to come to a solution. In particular, logic, probability and statistics, and algebra are all fields in which problem solving is a key factor. Math is used as a stepping stone to more complex ideas to answer questions in everyday life. The question below is a classic example of how logical thinking and mathematical knowledge can be used to come to a solution to situation that may seem to have a random outcome to the untrained eye.
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Do you switch doors? Why or why not?