Easy problem
Wednesday, June 25, 2008
Pick a number, any number. If the number is even, divide it by 2; if the number is odd, multiple it by 3 and add 1. Now, take the resulting number from the applied rule and continue the rule. Eventually, you will hit 1.
The actual problem:
is it true that any number you pick, for which the rules above are applied, will eventually reach the number 1?Seems easy enough. And it's either true or false. For example, lets start with 6. Our sequence is then 3, 10, 5, 16, 8, 4, 2, 1. If you try it with other numbers, chances are that you will reach 1.
So, it's true enough. Or is it?
This is one of those easy-to-state number theory problems which no one has been able to
prove.
Comments:
I was sure I could do it - it seemed easy enough...But apparently the one advanced math class I took in college wasn't enough to allow me to solve a problem that professional mathematicians couldn't do...I do think that it's solvable, and I bet it's done by an amateur instead of some expert - it's probably going to be something reasonably simple.