In her boldest move, Goddard put her full name at the bottom of all the copies of the Declaration that her printing presses churned out and distributed to the colonies. It was the first copy young America would see that included the original signers’ names — and Congress commissioned her for the important job.
In 2010, programmers found that a 3x3x3 Rubik’s cube can be solved in a maximum of 20 moves from any starting position, no matter how scrambled.
A year later, Demaine, Eisenstat and their colleagues devised a formula to solve a Rubik’s cube with sides of any length and found that the number of moves required for a cube of side n is proportional to n2/log n.
Finding the number for a cube with n=3 took several years of computing time and Demaine estimates that the n=4 case would take billions of times longer. “I conjecture it will never be fully solved,” he says.
This is the upper limit for the most scrambled cubes, but many cubes will not take that long. Figuring out whether any given configuration of a cube will take fewer moves is tricky. “We know an algorithm to solve all cubes in a reasonable amount of time,” Demaine says. “But if I give you a particular configuration of the cube, and then you want to solve it with the fewest moves for that configuration, that’s really tough.”