An Unsolved Mystery — the Collatz Conjecture!

Transcript

An Unsolved Mystery — the Collatz Conjecture! The Collatz Conjecture is described as "one of the most famous unsolved problems in mathematics". It's a process that starts with any whole number and follows two simple rules to create a sequence of new numbers. The Rules of the Conjecture The process, as laid out in the text, is as follows: Start with any whole number. If the number is even, you divide it by 2. If the number is odd, you multiply it by 3 and add 1. You then take the result and repeat the process. An Example Let's follow the book's example starting with the number 12: 12 is even, so we divide by 2: 12 / 2 = 6 6 is even, so we divide by 2: 6 / 2 = 3 3 is odd, so we multiply by 3 and add 1: (3 × 3) + 1 = 10 10 is even, so we divide by 2: 10 / 2 = 5 5 is odd, so we multiply by 3 and add 1: (5 × 3) + 1 = 16 16 is even, so we divide by 2: 16 / 2 = 8 8 is even, so we divide by 2: 8 / 2 = 4 4 is even, so we divide by 2: 4 / 2 = 2 2 is even, so we divide by 2: 2 / 2 = 1 Once the sequence reaches 1, it gets stuck in a loop (1 -> 4 -> 2 -> 1...). Other examples of Sequences are 12, 6, 3, 10, 5, 16, 8, 4, 2, 1 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 21, 64, 32, 16, 8, 4, 2, 1 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 The Unsolved Mystery The "conjecture," which was proposed by mathematician Lothar Collatz in 1937, is the idea that no matter what whole number you begin with, the sequence will always eventually reach 1. Even though mathematicians have tested this for countless numbers and have never found one that fails, no one has been able to create a mathematical proof that it is true for all numbers. This is why it remains one of mathematics' great unsolved mysteries.