The Universe of Discourse

A maybe-interesting number trick?

I'm not sure if this is interesting, trivial, or both. You decide.

Let's divide the numbers from 1 to 30 into the following six groups:

Choose any two rows. Chose a number from each row, and multiply them mod 31. (That is, multiply them, and if the product is 31 or larger, divide it by 31 and keep the remainder.)

Regardless of which two numbers you chose, the result will always be in the same row. For example, any two numbers chosen from rows B and D will multiply to yield a number in row E. If both numbers are chosen from row F, their product will always appear in row A.

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