10 · Interrogate the referee's card

The actual thirteen-row card this repository found. Click columns to choose four of them.

Try this. Choose any four columns you like, adversarially. Some row always shows both symbols inside your chosen columns; the tests check all seventy choices, and you will not find a counterexample.

Thirteen rows of coin flips suffice at this toy size, and almost any random card passes here. At the real sizes nothing can be checked case by case, and two counting arguments do the work instead.