To maximize your chances of winning in this game, where you have to guess either 0 or 11 out of the 22 numbers (from 1 to 22), and you have 9 guesses, your strategy should focus on maximizing the chances of hitting the right number while minimizing overlap between your guesses. Here's a step-by-step breakdown:

Step 1: Understand the Goal

• 0 means you must guess no numbers correctly.
• 11 means you must guess exactly 11 numbers correctly.

You are given 9 guesses, which means you can choose 9 numbers out of 22, and the game has to decide whether your guesses match 0 or 11 of the total 22 numbers.

Step 2: Divide the 22 Numbers into Two Groups

To maximize your chances, consider dividing the 22 numbers into two distinct groups:

• One group for your guesses, and
• Another group for the numbers you don't guess.

Given that you need to choose 9 guesses, you want to split the 22 numbers efficiently. Let's say:

• Group A (guessed numbers): 9 numbers (your guesses).
• Group B (non-guessed numbers): 13 numbers (the remaining numbers that you don't guess).

Step 3: Strategy Based on the Outcome

1. If the answer is 0 (none of your guesses are correct):

   • All of your 9 guesses must be from Group A, and none of them should match the actual set of correct numbers (which are from Group B).

2. If the answer is 11 (exactly 11 numbers are correct):

   • 11 numbers will be part of your guesses (from Group A), and the other 11 numbers will come from the remaining non-guessed numbers (Group B).

You must try to split the set of 22 numbers in such a way that you maximize the chances of getting 0 or 11 numbers matching with your guesses.

Step 4: Maximizing Probability

The best strategy would be to ensure that your 9 guesses are spread in a way that balances both outcomes equally. This way, if the answer is 0, you don't overlap too much, and if it's 11, you're more likely to have a full 11-number match.

Quick Recap:

• Divide the numbers into two groups: one with your guesses and one with the non-guessed numbers.
• Your guesses should ideally be spaced out to ensure that whether the correct set is 0 or 11, you maximize the chances for each outcome.

Does that make sense? Would you like to dive into deeper probabilities or simulations of this? Let me know if you'd like more clarity!

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5 Related Questions:

1. How do probability distributions apply to this type of guessing game?
2. What are some ways to simulate different guessing strategies to measure success?
3. How could I optimize my guesses for the case where 11 numbers must be correct?
4. Could a Monte Carlo simulation help in this game to test different strategies?
5. How would you modify the strategy if you had more or fewer guesses?

Tip:

To help visualize your chances, try creating a simple simulation or use an online tool to calculate probabilities for your guesses!