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When taking a polynomial modulo
For completeness, the linear term's coefficient should also get reduced in the same way as the constant term, so that
Consider the attached tree.
You start from the root, and with each level you create a sub-branch for each of the choices you have.
So, the root has two children, white and multigrain bread.
Each of those children has three children, because you have three meat choices
Each of those children has two children, because you have two cheese choices.
Then, you identify all the sandwiches by choosing a leaf, and read the label that lead you there.
For example, leaf number 4 represents a sandwich with white bread, turkey and provolone.
