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The Queen’s Gambit, And…

People have been trying hard to solve the problem for 150 years, and finally, a Harvard Mathematician has solved the puzzle, related to the Queen, mathematically. Apparently, it is assumed that the 150-year-old problem on the chessboard has probably been solved this time.

The Queen’s Gambit is one of the oldest openings in a game of chess, which starts with the moves 1.d4 d5 2.c4, and is still commonly played today. It is traditionally described as a Gambit because the White appears to sacrifice the c-pawn; however, this could be considered a misnomer as the Black cannot retain the pawn without incurring a lot of disadvantage.

As per this method, a player puts the pawn, sitting just in front of the White Queen, two blocks (d-4) ahead. In the same way, the opponent player moves forward the pawn, sitting in front of the Black Queen, two steps (d-5). In the second move, the first player moves the pawn, sitting in front of the White Bishop, forward two steps (c-4). Naturally, the Black pawn can check the White pawn in c-4. However, such a move leaves the centre or middle portion of the board completely vulnerable for the Black pawn. The d-4, d-5, c-47 is one of the oldest and most popular methods in the history of chess, and it is famously known as Queen’s Gambit, worldwide. It may be noted that there is also a novel of the same name, which has recently gained widespread popularity as a Web Series.

Queen’s Gambit

The puzzle was somewhat like this: How many times the eight conflicting Queens can move forward without attacking each other on a 64-block chessboard? A German chess magazine had raised this question way back in 1848. A couple of years later, masters of the game claimed that a total of 92 moves could be made in which none of the eight Queens would attack one another. However, the more complicated form of this problem appeared in 1869, which saw the query: What if one places an even larger number of Queens on a chessboard of the same relative size, say, 1,000 Queens on a 1,000-by-1,000-square chessboard, or even a million Queens on a similarly sized board?

Dr Michael Simkin, a Post-Doctoral Fellow and a Mathematician at Harvard University’s Centre of Mathematical Sciences and Applications, has come up with a near perfect solution. After working on the n-Queens mathematical problem for nearly five years, he has come to the conclusion that there is a way in a chessboard with an infinite number (or (0.143n)^n (where n = the number of Queen)) of blocks, where no Queen will attack one another. The mathematician has explained that there are about (0.143n)n ways the Queens can be placed so none are attacking each other on giant n-by-n chessboards. His final equation doesn’t provide the exact answer, but instead simply says that this figure is as close to the actual number as one can get right now. The 0.143 figure, which represents an average level of uncertainty in the variable’s possible outcome, is multiplied by whatever ‘n’ is and then raised to the power of ‘n’ to get the answer.

Dr Michael Simkin

In an article, titled A Different Kind of Queen’s Gambit (published in The Harvard Gazette on January 21, 2022), Juan Siliezar wrote: “On the extremely large chessboard with one million Queens, for example, 0.143 would be multiplied by one million, coming out to about 143,000. That figure would then be raised to the power of one million, meaning it’s multiplied by itself one million times. The final answer is a figure with five million digits.

Dr Simkin, admittedly a terrible chess player, is trying to improve upon his game. He stressed: “I guess, math is more forgiving. If you were to tell me I want you to put your Queens in such-and-such way on the board, then I would be able to analyse the algorithm and tell you how many solutions there are that match this constraint. In formal terms, it reduces the problem to an optimisation problem.

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