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A single bet consists of predicting the result of $n$ games, where each game has $3$ different possible outcomes: win, draw, loss.

Given a set of guesses for each game, I want to calculate the minimum number of bets that can guarantee the second prize (i.e., hit $n-1$ games).

I don't need a detailed explanation on how to achieve that, just where to look for.

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  • $\begingroup$ I would not know "where to look." It might not be too difficult to work out the "wheel" that you ask for, though. $\endgroup$ – hardmath Mar 30 at 21:40
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What you want is also known as a ternary covering code. Your case is often referred to in the literature as the Football pools problem. The Wikipedia article also has the best known bounds for $n\le 14$. See the $R=1$ column of this table for citations on where those bounds cam form.

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