A Number Chain is created by having a rule that takes any number to some other (not necessarily different) number. Then we start somewhere and see where we end up.

For example:

• if every number gets doubled,
• if every number gets halved (rounding up),
• every number chain ends with 1.
• if every number gets halved (rounding down),
• every number chain ends with 0.
Now suppose we use the following rule:
• If n is even, halve it.
• If n is odd, send it to 3n+1
Questions:
• Where does 7 go?
• Where does 17 go?
• Where does 27 go?
• What are the possibilites?
• Where does -5 go?
It is an unproven conjecture that every positive number eventually ends at 1.