P versus NP problem
How hard is it to solve, outright? If one starts with just 100 rocks, there are 2^{100-1}-1 = 633,825,300,114,114,700,748,351,602,687, or about 6.3 x 10^{29} possible ways (combinations) to divide these rocks into two piles. If one could check one unique combination of rocks every day, it would take 1.3 x 10^{22} or 1,300,000,000,000,000,000,000 years of effort. For comparison, physicists believe that the universe is about 1.4 x 10^{10} years old (450,000,000,000,000,000 or about 4.5 x 10^{17} seconds, or about one trillionth as old as the time it would take for our rock piling effort. That means that if one takes all of the time that has passed since the beginning of the universe, one would need to check more than two trillion (2,000,000,000,000) different ways of dividing the rocks every second, in order to check all of the different ways.