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Advent calendar 2022

3 December

Write the numbers 1 to 81 in a grid like this:
$$ \begin{array}{cccc} 1&2&3&\cdots&9\\ 10&11&12&\cdots&18\\ 19&20&21&\cdots&27\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ 73&74&75&\cdots&81 \end{array} $$
Pick 9 numbers so that you have exactly one number in each row and one number in each column, and find their sum. What is the largest value you can get?

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