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1.2: Logic Puzzles

  • Page ID
    23872
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    Clear thinking (or logic) is important not only in mathematics, but in everyday life, and can also be fun; many logic puzzles (or brain teasers) can be found on the internet or in bookstores. Here are just a few. Solving problems like these provides good practice for some of the logic skills that will be needed later in this book.

    Exercise \(\PageIndex{1}\)

    There was a robbery in which a lot of goods were stolen. The robber(s) left in a truck. It is known that:

    1. No one other than A, B and C was involved in the robbery.
    2. C never commits a crime without including A as an accomplice.
    3. B does not know how to drive.

    So, can you tell whether A is innocent?

    Exercise \(\PageIndex{2}\)

    On the island of Knights and Knaves,1 every resident is either a Knight or a Knave (and they all know the status of everyone else). It is important to know that:

    • Knights always tell the truth.
    • Knaves always lie.

    More precisely, every assertion spoken by a Knight is true, and every assertion spoken by a Knave is false.

    You will meet some residents of the island, and your job is to figure out whether each of them is a Knight or a Knave.

    1. You meet Alice and Bob on the island. Alice says “Bob and I are Knights.” Bob says, “That’s a lie! She’s a Knave!” What are they?
    2. You meet Charlie, Diane, and Ed on the island. Charlie says, “Be careful, not all three of us are Knights.” Diane says, “But not all of us are Knaves, either.” Ed says, “Don’t listen to them, I’m the only Knight.” What are they?
    3. You meet Frances and George on the island. Frances mumbles something, but you can’t understand it. George says, “She said she’s a Knave. And she sure is — don’t trust her!” What are they?

    Exercise \(\PageIndex{3}\)

    Complete each of these mini-Sudoku puzzles, by putting a number from 1 to 4 in each box, so that no number appears twice in any row or column, or in any of the four \(2 \times 2\) boxes with dark outlines. (Each of the puzzles has a unique solution.)

    1) 2) 3)
    Sudoku 1.PNG Sudoku 2.PNG Sudoku 3.PNG

    Exercise \(\PageIndex{4}\)

    In a game similar to Mastermind, one player chooses a secret \(4\)-digit number, using only the digits 1–6, inclusive. (Repeated digits are allowed.) The other player makes a series of guesses. After each guess, the first player tells the other how many of the digits are in the guess are perfectly correct, and how many of the other digits are correct, but in the wrong place. In each of the following games, there is now enough information to determine the secret number. Figure out the secret number.

    1.

    Guess # Correct # In Wrong Spot
    1234 0 3
    2354 0 3
    3642 1 1
    5143 0 3
    4512 1 2
      4 0

    2.

    Guess # Correct # In Wrong Spot
    1234 0 2
    4516 1 2
    4621 1 1
    6543 0 2
    5411 0 3
      4 0

    This page titled 1.2: Logic Puzzles is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dave Witte Morris & Joy Morris.

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