Enya_and_WeirdAl_fan Posted December 27, 2019 Report Share Posted December 27, 2019 Hi. I have a question of nomenclature. Is there a name given for a particular set of 4 cells from an otherwise empty 4x4 grid, having the property that they include ONE cell in each row, ONE cell in each column, and ONE cell in each of the two main diagonals? An example: ╔════╤════╤════╤════╗ ║ ▓▓ │ │ │ ║ ╟────┼────┼────┼────╢ ║ │ │ ▓▓ │ ║ ╟────┼────┼────┼────╢ ║ │ │ │ ▓▓ ║ ╟────┼────┼────┼────╢ ║ │ ▓▓ │ │ ║ ╚════╧════╧════╧════╝ I hope the above figure shows up well in your display. You may wish to copy all this and paste it into a simple text editor and using the UTF-8 text encoding, as well as a fixed-pitch font. Anyway, I've been referring to such sets of 4 as challenger configurations, which I named after a daily puzzle I used to do, carried in some newspapers, called the Challenger. They would show a mostly empty 4x4 grid with totals displayed for each row, column, and both diagonals, as well as 4 given numbers. The challenge was to fill in the remaining 4x4 grid cells each with a choice of number from 1 to 9 so as to make the totals correct. There was also a challenge time in which to complete the task. Now I figure that about 99% of the time the POSITIONS of the grid for the given numbers would, like the configuration shown above, include one of the given numbers by itself in a corner, one of the given numbers by itself on an outer edge, and the other two given numbers diagonally adjacent to each other, both of their positions on the grid being a chess knight's jump from the lone edge, and one of them also being a knight's jump from the lone corner. For there to be ONE given number in each row, and in each column, and in both of the two main diagonals, the POSITIONS would HAVE to be as I've described. Anyway, shall I continue to refer to it as a challenger configuration, or have mathematicians already chosen a name for one of these configurations? Quote Link to comment Share on other sites More sharing options...

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