Double Latin Squares

Double Latin Squares

A Latin square is an \(n \times n\) square grid in which each row and each column has the numbers from \(1\) to \(n\). (It does not need to be numbers, it could be letters or colors or anything else.) A double Latin square is an \(n \times n\) grid in which each row and each column has each of \(n\) numbers and each of \(n\) colors. Additionally, each number appears once with each color.

The goal of this puzzle to to make a double Latin square on the right for each value of \(n\), or show that it is impossible to do it for that \(n\).

To move a colored number from the left grid to the right grid, click on a number in the left grid to select it, then click on a space in the right grid to place it. If you subsequently click on another space on the right it will move the currently selected colored number to the new position. To remove a number, double-click it or use the erase button.

Use the numbers below the left board or the colors to its left to place a number or color in the right grid without both. Click two circles below or to the right of the right board to interchange two columns or rows. Click on the the double arrow button to flip the grid along the diagonal.

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Supported in part by NSF Grant #1123255