The 3N problem

Click here to launch the SNAP! program-based lab assistant.


You and your noted mathematician colleagues convene in (virtual) Geneva to present brilliant theories pertaining to one of the world’s great mysteries, the elusive 3n Problem.


The 3N problem offers a fantastic world of exploration for learners of all ages. (I have done this with kids as young as the third grade.)

The problem is known by several other names, including: Ulam’s problem, the Hailstone problem, the Syracuse problem, Kakutani’s problem, Hasse’s algorithm, Thwaite’s Conjecture 3X+1 Mapping and the Collatz problem.

The 3N problem has a simple set of rules. Put a positive integer (1, 2, 3, etc…) in a “machine.” If the number is even, cut in half – if it is odd, multiply it by 3 and add 1. Then put the resulting value back through the machine. For example, 5 becomes 16, 16 becomes 8, becomes 4, 4 becomes 2, 2 becomes 1, and 1 becomes 4. Mathematicians have observed that any number placed into the machine will eventually be reduced to a repeating pattern of 4…2…1…

3n machine

This observation has yet to be proven since only a few billion integers have been tested. The 4…2…1… pattern therefore remains a conjecture.

The computer will serve as your lab assistant – smart enough to work hard without sleep, food or pay, but not so smart that it does the thinking for you. It will collect data and represent it in three different ways for you.

Click here to launch the SNAP! program-based lab assistant.