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1

A problem must surely demonstrate the finiteness of the board if it has two twins, the solutions are essentially different, and the twinning is by shifting every unit 1 file to the right. Or, regarding the units as fixed, by cutting the empty h-file off the right-hand side and pasting it to the left-hand side. [Title "Heinz Däubler. Augsburger ...


1

As an applied mathematician, I feel that mathematics very seldom solves any problem in a practical sense, apart from those that reduce to some form of counting. There are many problems that lead to differential equations, for example, that present points of interest in their own right, but to apply them to any real engineering situation assumptions must be ...


2

This answer spells out the actual calculation of performance rating for USCF tournaments, as in the June 2017 Rating Estimator that Fred Knight's answer points to. If you view the page source at that link, the calculation is given in the form of the code for the performanceRating function. Aside from details about whether one has an established rating and ...


5

60 unoriginal pawn moves can be made in a game by quadrupling the pawns 4 times. One can use the same capture once in each column of 4. Then you can use the exact same move 1+3+3+3+3 times in each column. And finally in the black columns white can make a move (to row 3) and vice versa Total: 15*4 =60 Here is an example game. [FEN ""] 1. Nc3 Nc6 2. ...


1

It is really difficult to find out legal positions but total positions possible is 13^64 , assuming each piece can be positioned in every available square


1

Is this possible when the lone knight starts only on certain squares ? If you stop and think about this for a second you will realize that the answer is obviously "Yes". If you have a "Knight's Tour" (that's what it is called) starting on square X then by definition it also goes through square Y (for all squares Y on the chessboard). ...


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