Harvard Mathematicians Solve 150 Years Old Chess Problem

Harvard Mathematicians Solve 150 Years Old Chess Problem

global.gerbangindonesia.org – Harvard Mathematicians Solve 150 Years Old Chess Problem

At first glance, at some point, chess seems like a simple game. There are 64 black or white squares, 16 pieces per side, and two competitors struggle to beat each other.

But if you dig deeper, this game offers very complex possibilities. In fact, the game presents challenges to chess theorists and mathematicians that can go unsolved for decades or even centuries.

In July 2021, one such challenge was finally solved. At least, solved up to a point.

The mathematician Michael Simkin of Harvard University in Massachusetts, focused on the n-queens problem that has puzzled scientists since it was first conceived in the 1840s.

If you know your chess, you know that the queen is the most powerful piece on the board, able to move any number of squares in any direction. The n-queen problem asks this: With a number of queens (n), how many arrangements are possible in which the queens are far enough apart that neither of them can eat the other?

For eight queens on a standard 8 x 8 board, the answer is 92. But what about 1,000 queens on a 1,000 x 1,000 square board?

How about a million queens? Simkin’s approximate solution to this problem is (0.143n)^n. Or, the number of queens is multiplied by 0.143, raised to the power of the number of queens.

It took Simkin almost five years to find this equation, with the various approaches and techniques used, and several obstacles on the way to the solution. In the end this Harvard mathematician was able to calculate the lower and upper bounds of the possible solutions using different methods, finding that these methods almost matched.

“If you tell me that I want you to place your queen this way and that on the board, then I will be able to analyze the algorithm and tell you how many solutions fit this constraint,” Simkin said.

“In formal terms, this reduces the problem to an optimization problem.”

The solution to the equation that Simkin found is not a completely correct answer to the n-queen problem, but it has provided an approximate answer that is as close as possible.

In theory, a more precise answer to the n-queen riddle should be possible again. But at least Simkin has brought us closer than ever, and he loves to challenge others to learn more.

“I think I may personally be done with the n-queen issue for a while, not because there’s nothing else to do with it but simply because I’ve been dreaming about chess and I’m ready to move on to get back on with my life again,” said Simkin.

In theory, a more precise answer to the n-queen riddle should be possible again. But at least Simkin has brought us closer than ever, and he loves to challenge others to learn more.

“I think I might personally be done with the n-queen issue for a while, not because there’s nothing else to do with it but simply because I’ve been dreaming about chess and I’m ready to move on to get back on with my life again,” said Simkin.

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