Examples of conjucture ???
Answers
One of the problems on those lists that I find the most interesting is the Collatz Conjecture. One version of the Collatz conjecture states that if you take a positive integer nn and do the following:
Divide by 2 if the integer is even
Multiply by 3 and add 1 if the integer is odd
you will eventually reach the number 1 by repeated iterations of steps 1 and 2.
One of the most interesting things about the Collatz Conjecture is that there appears to be no pattern in the number of iterations it takes to reach the number 1. For example, the number n=19n=19 takes 20 steps to reach 1, while the number n=27n=27 takes 111 steps to reach 1.
It is also interesting that the Generalized Collatz Problem is recursively undecidable (which you can read about here), while the Collatz Problem from above remains unsettled.