An elegant math problem that inspires lovely visuals and lively holiday conversation.

The Collatz Conjecture (also known as the 3 n + 1 problem, the Ulam conjecture, or the Hailstone problem) was introduced by Lothar Collatz in 1939. The conjecture starts with a process:

- Choose any number.
- If it is even, divide it by 2.
- If it is odd, multiply it by 3 and then add 1.
- Repeat with the new number.

*For example:*

^{60}, but currently there is no formal proof that you always get to 1.

Whether you are talking with your astrophysicist aunt or 4th grade nephew, you can dazzle them with The Collatz Conjecture. Try asking them:

- Can you believe that they've never been able to prove this?
- Which visual pattern do you like the most and why?
- Can you beat me to the 4-2-1 sequence when starting with the number 33? (no calculators allowed)
- What's your favorite math problem?
- What's the greater meaning of this numeric pattern?

Jeffrey P. Dumont and Clifford A. Reiter, *Real Dynamics Of A 3-Power Extension Of The 3x+1 Function*, Dynamics of Continuous, Discrete and Impulsive Systems: A Mathematical Analysis, 10 (2003) 875-893

Jeffrey P. Dumont and Clifford A. Reiter, *Visualizing Generalized 3x+1 Function Dynamics*, Computers & Graphics, 25 5 (2001) 883-898