Application of Latin Squares
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There are 36 officers, six officers of six different ranks in each of 6 regiments. Find an arrangement of the 36 officers in a $6times 6$ square formation such that each row and each column contains one and only one officer from each regiment of each rank. (from Euler).
Dear math stack exchange family, can you help me interpreting this word problem in Latin squares?
latin-square
asked Dec 7 '18 at 22:17
NANINANI
11
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add a comment |
$begingroup$
There are 36 officers, six officers of six different ranks in each of 6 regiments. Find an arrangement of the 36 officers in a $6times 6$ square formation such that each row and each column contains one and only one officer from each regiment of each rank. (from Euler).
Dear math stack exchange family, can you help me interpreting this word problem in Latin squares?
latin-square
asked Dec 7 '18 at 22:17
NANINANI
11
$endgroup$
$begingroup$
The ranks, when numbered 1 thru 6, form a Latin square. As do the regiments. Furthermore, because each regiment sends in exactly one office of each rank, the two Latin squares must be orthogonal (=MOLS)
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:26
2
$begingroup$
And see for example here for discussion on the impossibility to place the officers as required. The puzzle is famous.
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:29
add a comment |
$begingroup$
There are 36 officers, six officers of six different ranks in each of 6 regiments. Find an arrangement of the 36 officers in a $6times 6$ square formation such that each row and each column contains one and only one officer from each regiment of each rank. (from Euler).
Dear math stack exchange family, can you help me interpreting this word problem in Latin squares?
latin-square
asked Dec 7 '18 at 22:17
NANINANI
11
$endgroup$
There are 36 officers, six officers of six different ranks in each of 6 regiments. Find an arrangement of the 36 officers in a $6times 6$ square formation such that each row and each column contains one and only one officer from each regiment of each rank. (from Euler).
Dear math stack exchange family, can you help me interpreting this word problem in Latin squares?
latin-square
latin-square
asked Dec 7 '18 at 22:17
NANINANI
11
asked Dec 7 '18 at 22:17
NANINANI
11
asked Dec 7 '18 at 22:17
NANINANI
11
asked Dec 7 '18 at 22:17
NANINANI
11
asked Dec 7 '18 at 22:17
NANINANI
11
11
$begingroup$
The ranks, when numbered 1 thru 6, form a Latin square. As do the regiments. Furthermore, because each regiment sends in exactly one office of each rank, the two Latin squares must be orthogonal (=MOLS)
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:26
2
$begingroup$
And see for example here for discussion on the impossibility to place the officers as required. The puzzle is famous.
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:29
add a comment |
$begingroup$
The ranks, when numbered 1 thru 6, form a Latin square. As do the regiments. Furthermore, because each regiment sends in exactly one office of each rank, the two Latin squares must be orthogonal (=MOLS)
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:26
2
$begingroup$
And see for example here for discussion on the impossibility to place the officers as required. The puzzle is famous.
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:29
$begingroup$
The ranks, when numbered 1 thru 6, form a Latin square. As do the regiments. Furthermore, because each regiment sends in exactly one office of each rank, the two Latin squares must be orthogonal (=MOLS)
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:26
$begingroup$
The ranks, when numbered 1 thru 6, form a Latin square. As do the regiments. Furthermore, because each regiment sends in exactly one office of each rank, the two Latin squares must be orthogonal (=MOLS)
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:26
2
2
$begingroup$
And see for example here for discussion on the impossibility to place the officers as required. The puzzle is famous.
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:29
$begingroup$
And see for example here for discussion on the impossibility to place the officers as required. The puzzle is famous.
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:29
add a comment |
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$begingroup$
The ranks, when numbered 1 thru 6, form a Latin square. As do the regiments. Furthermore, because each regiment sends in exactly one office of each rank, the two Latin squares must be orthogonal (=MOLS)
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:26
2
$begingroup$
And see for example here for discussion on the impossibility to place the officers as required. The puzzle is famous.
$endgroup$
– Jyrki Lahtonen
Dec 7 '18 at 22:29