An Unsolved Mystery — the Collatz Conjecture
Look at the sequences below—the same rule is applied in all the sequences:
a. 12, 6, 3, 10, 5, 16, 8, 4, 2, 1
b. 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
c. 21, 64, 32, 16, 8, 4, 2, 1
d. 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
Do you see how these sequences were formed?
The rule is: one starts with any number; if the number is even, take half of it; if the number is odd, multiply it by 3 and add 1; repeat.
Notice that all four sequences above eventually reached the number 1. In 1937, the German mathematician, Lothar Collatz conjectured that the sequence will always reach 1, regardless of the whole number you start with. Even today—despite many mathematicians working on it — it remains an unsolved problem as to whether Collatz’s conjecture is
Make some more Collatz sequences like those above, starting with your favourite whole numbers. Do you always reach 1?
Do you believe the conjecture of Collatz that all such sequences will eventually reach 1? Why or why not?
Collatz sequence starting with whole number 15 is as follows: 15,
Collatz sequence starting with whole number 7 is as follows: 7,