We were presented with an unsolved mathematical dilemma known as the 3N problem. According to Daniel Pink's A Whole New Mind, a right brainer like myself approaches the problem by "seeing all the elements of a situation and understanding what they mean". I definitely had to process the different attributes of the problem to gain a better understanding of the task at hand.  My initial steps included a thorough analysis of the graphing tool provided by the Microworlds Ex software, researching the problem, and enlisting others in the process. One site called the 3N an "unsolved mathematical challenge and a taste of chaos" but the visual provided by the site helped clarify the problem. The graph demonstrated how the numbers peaked and dropped numerous times until the 4-2-1 pattern occured infinitely. This is the site that I found helpful:
http://www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=6...
I began with the number 148, 21 generations occurred before it arrived at the infinite 4-2-1 pattern. What is the correlation between 148 and 21 generations?  I randomly selected numbers divisible by 4 to see if I could locate a possible pattern.

Tested number:      Generations:
20                            5
16                            2
12                            7
 8                             1
 4                             0

20/4=5
16/4-2=2
12/4+4=7
8/4-1=1
4/4-1=0

This background information was created by Pepperdine professor Gary Stager.

BACKGROUND

The 3N problem offers a fantastic world of exploration for learners of all ages.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...

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.