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Ramsey Numbers: A Problem of Galactic Proportions
When aliens attack, do you do the math or fight back?
Some numbers are hard to compute.
In a 1990 article for Scientific American, mathematicians Ronald Graham and Joel Spencer quoted Paul Erdös as saying:
Suppose aliens invade the earth and threaten to obliterate it in a year’s time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world’s best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack.
It’s an intriguing quote. But what the heck is a Ramsey number, and why is it so hard to calculate?
The Game of Sim
Let’s start by playing a game.
The game is called Sim — a two-player game that you can play with pencil and paper. Every game of Sim is played on a “board” made from the six vertices of a hexagon:
