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## #1 2019-12-26 04:54:16

Enya_and_WeirdAl_fan
Member
Registered: 2019-12-26
Posts: 2

### Does what I call a Challenger configuration have another name already?

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?

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## #2 2019-12-27 15:20:25

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,956
Website

### Re: Does what I call a Challenger configuration have another name already?

Hi;

Is this related to https://en.wikipedia.org/wiki/Block_design

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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