Bagels

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A long time ago (around 1974) when I was in high school, I learned a logic game called Bagels. The board game Mastermind uses very similar rules, but you don't need any props to play this game. This game was developed by D. Resek and P. Rowe of the Lawrence Hall of Science and Math in Berkeley and is documented in the book named Family Math.

The game is deceptively simple. If you play well though, it can be fairly deep.

Do you want to take the role of choosing a number or guessing my number?

Rules:

1. There are two opponents. One picks a number, and the other one attempts to guess the number. The person picking the number must give accurate answers to the guesses.
2. The person picking a number picks a three digit number. In this version, there may be no leading zeros, and digits may not be repeated.
3. The person guessing the number gives three digit numbers.
4. The person who picked the number answers:
• Fermi -- One of the digits in the guess matches one of the digits in the answer, and it is in the right position.
• Pico -- One of the digits in the guess matches one of the digits in the answer, but the digit is not in the right place.
• Bagels -- None of the digits in the guess match any of the digits in the answer.
Multiple answers may come out of a single guess. For examples, look at the table below: