The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it: the 2 is found by adding the two numbers before it (1+1), the 3 is found by adding the two numbers before it (1+2), the 5 is (2+3), and so on! Who is Fibonacci? His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy. "Fibonacci" was his nickname, which roughly means "Son of Bonacci". By the way, Fibonacci was not the first to know about this sequence, it was known in India hundreds of years before! Problem 1: The Fibonacci sequence starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits(0-9) is the last to appear in the units position of a number in the Fibonacci sequence? Problem 2: Somebody puts one pair of rabbits in a field surrounded by walls so none will escape. How many pairs will be born from that pair in one year if they bear a new pair in each month, and in the second month those newborn pairs start to reproduce?
