She entered the scores in random order into a spreadsheet, which recalculated the class average after each score was entered. Walter gave an exam in a mathematics class of five students. If the pattern were continued, how many nonoverlapping unit squares would there be in figure 100?

How many positive integers have the property that is a positive integer?įigures, ,, and consist of, ,, and nonoverlapping unit squares, respectively. When their sum is subtracted from their product, which of the following numbers could be obtained? Two different prime numbers between and are chosen. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence? The Fibonacci sequence starts with two 's, and each term afterwards is the sum of its two predecessors. How many jellybeans were in the jar originally? What is the largest possible value of the sum ?Įach day, Jenny ate of the jellybeans that were in her jar at the beginning of that day. Let and be distinct positive integers such that the product. In the year, the United States will host the International Mathematical Olympiad.