• Brain Teasers & Puzzles

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    • A park contains paths that intersect at various places.  The intersections all have the properties that they are 3-way intersections and that, with one exception, they are indistinguishable from each other.  The one exception is an intersection where there is a restaurant.  The restaurant is reachable from everywhere in the park.  Your task is to find your way to the restaurant.

      The park has strict littering regulations, so you are not allowed to modify the paths or intersections (for example, you are not allowed to leave a note an intersection saying you have been there).  However, you are allowed to do some bookkeeping on a pad of paper that you bring with you at all times (in the computer-science parlance, you are allowed some state).  How can you find the restaurant?

      You may assume that once you enter an intersection, you can continue to the left, continue to the right, or return to where you just came from.

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    • Given is a (possibly enormous) rectangular chocolate bar, divided into small squares in the usual way. The chocolate holds a high quality standard, except for the square in the lower left-hand corner, which is poisonous. Two players take turns eating from the chocolate in the following manner: The player whose turn it is points to any one of the remaining squares, and then eats the selected square and all squares positioned above the selected square, to the right of the selected square, or both above and to the right of the selected square. Note, although the board starts off rectangular, it may take on non-rectangular shapes during game play. The object of the game is to avoid the poisonous square. Assuming the initial chocolate bar is larger than 1×1, prove that the player who starts has a winning strategy.

      Hint: To my knowledge, no efficient strategy for winning the game is known. That is, to decide on the best next move, a player may need to consider all possible continuations of the game. Thus, you probably want to find a non-constructive proof. That is, to prove that the player who starts has a winning strategy, prove just the existence of such a strategy; in particular, steer away from proofs that would construct a winning strategy for the initial player.

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    • You are given an irreflexive symmetric (but not necessarily transitive) “enemies” relation on a set of people.  In other words, if person A is an enemy of a person B, then B is also an enemy of A.  How can you divide up the people into two houses in such a way that every person has at least as many enemies in the other house as in their own house?

      Hint:  Planar configuration of straight connecting lines puzzle may provide a hint to solving this puzzle.

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    • Given an even number of points in general positions on the plane (that is, no three points co-linear), can you partition the points into pairs and connect the two points of each pair with a single straight line such that the straight lines do not overlap?

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    • Someone picks, at their will, two cards from a deck of cards. The cards have different numbers, so one is higher than the other. (In other words, the person picks two distinct numbers in the inclusive range 1 through 13.)  The cards are placed face down on a table in front of you.  You get to choose one of the cards and turn it face up.  Now, you will select one of the two cards (one of whose face you can see, the other one you can’t).  If you select the highest card, you win.  Design a card-selection strategy for which your chance of winning is strictly greater than 50%.

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    • Fill in the clues to reveal the hidden message, in this holiday and cold weather puzzle, from us to you.

      Using the clues given, fill in the grid boxes with the answers. In the grid, each horizontal row is one clue and the clues should be entered from the top down. So the first horizontal row goes with clue 1, the second horizontal row goes with clue 2, etc. When the grid is complete, read the highlighted boxes from top to bottom for the hidden message.

      HINT: Some of the clues are one word, some are two. Don’t leave spaces between the words when entering a two word answer.

      1. The Coldest Season of the Year
      2. Spicy, hot drink to ward off chills
      3. For kissing your beau under
      4. A hot stone for your feet & a horse to pull you through the snow
      5. Zipping down the mountain trails, diamond back to bunny hill
      6. Warmers for your hands
      7. Tasty drink that’s good with brandy & nutmeg added
      8. These sparkling beauties are nature made
      9. Green trailing plant
      10. The cookie that makes a house
      11. Festive greens for your front door
      12. Red & white sticks of pure pleasure
      13. No two alike they mantle the ground in cold weather
      14. Pretty plants with red leaves that form the flower
      15. Something for the fireplace
      16. Father Time and Baby _____ ________
      17. Long tailed headgear with a pompom on the end
      18. Waltzing around the icy pond
      19. Gaily wrapped with a bright red bow
      20. This cake like dessert can be made using the real fruit
      21. This plant has sharp green leaves and little red berries
      22. String these on the trees – inside and out
      23. Three balls of snow, a felt hat and a carrot nose
      24. The horses prance while wearing these
      25. An Eskimo’s house
      26. Down the hill on the snow – whee!
      27. Sing a merry song to your neighbors
      28. If you go to one you should bring a gift for the hostess

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    • Each of the following phrases below describes the name of a popular game. The dashes on the left side of each phrase represent the name of the game the phrase describes (Note: one dash is one letter, a space signifies a new word). Can you decipher the name of each of the games below?
      (Hint: Not all of the clues pertain to the game itself. Some of the clues refer to the actual meaning of the word or phrase by which the game is named. Also, some of the games are board games, some card games, and some are games designed for a group of people.)

      1. _ _ _ _ _ an African game using beans (1 word)
      2. _ _ _ _ _ capture the king to win the game (1 word)
      3. _ _ _ _ _ _ _ _ jump over the men to crown a king (1 word)
      4. _ _ _ _ _ _ _ turning over the two-colored piece is the name of the game (1 word)
      5. _ _ _ _ _ _ _ _ _ _ _ it crashed in 1929 (2 words)
      6. _ _ _ _ _ with deepest apologies (1 word)
      7. _ _ _ _ _’_ _ _ _ a successful overthrow or takeover (2 words)
      8. _ _ _ _ _ _ _ _ a dictionary helps with this game (1 word)
      9. _ _ _ _ _ _ _ _ _ _ a French card game where mileage counts (2 words)
      10. _ _ _ _ you only have one (1 word)
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    • Each of the following phrases below describes the name of a popular game. The dashes on the left side of each phrase represent the name of the game the phrase describes (Note: one dash is one letter, a space signifies a new word). Can you decipher the name of each of the games below?
      (Hint: Not all of the clues pertain to the game itself. Some of the clues refer to the actual meaning of the word or phrase by which the game is named. Also, some of the games are board games, some card games, and some are games designed for a group of people.)

      1. _ _ _ _ _ _ _ _ _ _ a dictionary of pictures (1 word)
      2. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Sherlock Holmes’ address (3 words)
      3. _ _ _ _ _ _ _ _ _ _ _ _ the police department of London (2 words)
      4. _ _ _ _ _ _ to puzzle or confuse the mind (1 word)
      5. _ _ _ _ _ _ _ _ _ _ _ _ _ to succeed, fail, or tie (3 words)
      6. _ _ _ _ _ _ _ _ a game of skill to win the flag (1 word)
      7. _ _ _ _ _ _ _ _ _ _ _ flip your chips to win the game (1 word)
      8. _ _ _ _ _ _ _ _ _ _ double or nothing (3 words)
      9. _ _ _ _ _ five card stud is one type (1 word)
      10. _ _ _ _ _ _ _ a type of storm (1 word)
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    • Each of the following phrases below describes the name of a popular game. The dashes on the left side of each phrase represent the name of the game the phrase describes (Note: one dash is one letter, a space signifies a new word). Can you decipher the name of each of the games below?
      (Hint: Not all of the clues pertain to the game itself. Some of the clues refer to the actual meaning of the word or phrase by which the game is named. Also, some of the games are board games, some card games, and some are games designed for a group of people.)

      1. _ _ _ _ _ _ _ _ _ _ _ _ _ _ the luck of life or just plain fate (3 words)
      2. _ _ _ _ _ _ _ _ _ _ _ _ _ _ the pursuit is purely trivial (2 words)
      3. _ _ _ _ _ _ ‘_’ _ _ _ _ _ _ _ going up or down? (3 words)
      4. _ _ _ _ _ _ _ _ do not pass go (1 word)
      5. _ _ _ _ some are calculated (1 word)
      6. _ _ _ _ Sherlock Holmes always finds them (1 word)
      7. _ _ _ _ _ _ _ _ _ uses the theme of Hansel and Gretal (1 word)
      8. _ _ _ _ _ _ _ _ dodge the board traps and laser fire to reach the flags first (2 words)
      9. _ _ _ _ _ _ _ _ exclamation or shout (1 word)
      10. _ _ _ _ _ _ _ _ honest people have them, liars don’t (1 word)
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    • Round 1- PuzzleFry

      Each of the clues below refers to a five-letter word that contains either ‘HI’ or ‘LO’ within it. Can you find all of them?

        1. dental care

       

        1. the sound a bird makes

       

        1. something a flower does

       

        1. \”Stop and _________.\”

       

        1. the navy has them

       

        1. how water comes from a faucet

       

        1. comes from a hen

       

        1. what you see if you hurt yourself

       

        1. something woven

       

        1. helps keep track of time

       

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