A problem is underconstrained when it has more unknowns than equations. When that happens there is not one solution but infinitely many, and the difficulty is no longer finding one. It is choosing.

The solution is not to choose. Have other people solve it for you.

The method is old and it works. In 1900 David Hilbert stood up in Paris and read out a list of problems he had not solved. There were twenty-three. He then sat down. Most of them were solved over the following century by other people, several of whom had not been born when he read the list. Hilbert is remembered as the man who solved mathematics for a hundred years. He had posed it.

Paul Erdős improved the method by attaching money. Twenty-five dollars for a small one, up to ten thousand for the large ones, payable on proof. He died in 1996 and the checks kept going out, written by a friend, for problems solved after the man who set them was gone. The money was real. The solving was done by others. The friend was Ron Graham, and he was doing it for free.

In 2000 the Clay Mathematics Institute put a million dollars on each of seven problems. One has been solved. The man who solved it declined the money. The method held: the problem was solved, by someone else, and the prize was never paid.

The Dugong Institute has posed ten. The prize is an undisclosed volume of Class-B notes, dispersed only upon the mapping of the Dugongian, and the notes bear the line "provided demand is never made." None of the ten has been solved. The solvers are warned on the cover of the first one that attempting it will make them forget what they were doing. This is the method in its purest form: the problem is posed, the prize is stated, and the only thing missing is anyone who can hold the problem in mind long enough to hand it to someone else.

On September 8 a company in San Francisco announced that ten thousand of its agents had solved a problem about the Navier–Stokes equations in eighty-eight hours, exchanging 4.9 million messages among themselves to do it. Nobody at the company read the messages. This is the newest form of the method and the one closest to its ideal, in which the other people are not people, and the problem is solved before anyone is told what it was.

Closer to home, the city runs a phone number. You describe the hole in the street and someone else fills it. Residents have been told for years that this is called reporting a problem. It is having other people solve it, and the city has three digits for it.

For a worked example see the brick building elsewhere in this issue. Nobody saw who built it. It is built.

Under Constrained also writes about problem solving.