“… If you take a positive integer, and then divide by 2 if it is even, or multiply by 3 and add 1 if it is odd, then repeat this process with the resulting number, eventually you will end up with the number 1 … A kid can understand the question, but no one can answer it.” …
Ha. I’ll bet we have CCers here who can figure this out.
Multiplying an odd number by 3 and adding one turns the resulting answer into an even answer, which then starts the dividing process. At some point, you will end up with a number in the geometric progression with a factor of 2… 1 2 4 8 16 32 64, etc… If you end up with any of those numbers, you can continue dividing by 2 until you hit 1.
I guess the real question is, where does that “some point” occur?
Intriguing. It looks so simple you’d think someone proved it a long time ago. All powers of 2 will result in 1 following the rule. All integers that results in a power of 2 will also result in 1 after applying the rule. All integers that will result in an integer that will result in a power of 2 will also result in 1. All integers that will result in an integer that will result in an integer that will result in a power of 2 will also result in 1. All integers that will result in an integer that will result in an… Now all I have to do is prove the sum of all these integers will be all integers 