How to make an algorithm to check if you have won on a Lotto?

Mathematics Asked by Jaakko Seppälä on November 28, 2020

I was wondering the following problem: Let us say that in a lotto you choose seven numbers from numbers $1$ to $39$. You want to have at least one winning row, that is, four or more correct numbers. To make sure you win, you choose many rows. Is there a faster algorithm to check if you make a winning set than take every single row and you check that if this row has at least four common elements with some of your rows? Because I found that on worst case that takes about $15380937cdot 329=5060328273$ checks as one has found that there is a set of $329$ rows to make sure you win What algorithm is a good to search a lotto design?.

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