New knowledge is often hard-won, to be gained only by protracted effort on the part of multiple workers, each responsible for some small advance. Occasionally, but importantly for those who compile trivia, the progress can be reported as a simple numeric value.

#### A case in point:

In 1981, Morwen Thistlethwaite proved that 52 were enough. Hans Kloosterman showed in 1992 that, actually, 42 would do. By 2010 it was known that in fact one can get by with as few as 20. What are they?

- Dietary nutrients needed for optimum health
- Gannet breeding pairs needed to establish a colony
- Moves needed to solve Rubik’s cube
- Syllables needed to communicate intelligibly

One might suppose that the Rubik’s cube toy invented by Ernö Rubik in 1974, however ingenious, is geometrically too simple to present much of an analytical challenge. Nevertheless, finding the minimum number of moves to solve the cube from any position was a hard-won achievement to which numerous mathematicians contributed. After Kloosterman, the upper bound continued to come down by successive degrees as new insights and tools were brought to bear. Michael Reid showed in 1995 that the final answer could not be less than 20, but it took 15 years more to prove that 20 moves would *always* suffice. That proof was presented in July, 2010 in a paper by Tomas Rokicki, Herbert Kociemba, Morley Davidson and John Detridge. Their approach combined careful problem analysis with a highly efficient approach to searching solution paths on the computer. Even then, the parallel processing power of cloud computing was needed to complete the demonstration in mere weeks rather than decades or centuries. (For more information, please see the source article at NextBigFuture.)