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  "body": "\n## Summary\n\nA Latin square of order $n$ is an $n \\times n$ array filled with $n$ symbols.\nEach symbol occurs exactly once in each row and exactly once in each column.\nLatin squares are the multiplication tables of quasigroups, and the Cayley tables of finite groups are examples.\nThey are used in the design of experiments and in coding theory, and orthogonal families of them are tied to finite projective planes.\nThe node [[Latin square|44HTG620GB]] gives the precise definition.\n\n## Explanations\n\n### L1 human\n\nA completed Sudoku grid is a Latin square of order $9$ with extra conditions on the boxes.\nWithout the boxes, the rule is only: no symbol repeats in a row or in a column.\nFor order $3$, the rows $1\\,2\\,3$, then $2\\,3\\,1$, then $3\\,1\\,2$ form a Latin square.\nEach new row is the previous row shifted by one place.\n",
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