Great Games: Pico Fermi Bagel

Pico Fermi Bagel is a guessing game for two players, or two teams, and uses quite a bit of strategy. Each player thinks of a number (use three digit numbers to begin with) and you take turns guessing the other person's number. Whoever guesses the other person's number first wins. With each player's guess, the other player must give clues. Use the clues in order to make a strategic next guess. There are three clues:

Pico means that one of the guessed digits is correct but is in the wrong place;

Fermi means that one of the guessed digits is correct and is also in the correct place;

Bagel means that none of the digits in the guess are correct.

Think Time: Abacus Beads

 

This diagram shows a simple abacus with nine beads representing the number 324.

a. If there are twenty beads and all must be used, what is the largest number that can be represented?

b. What is the smallest number that can be represented?

c. If there are almost the same number of beads on each column, what numbers can be represented?