• Brain Teasers & Puzzles

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    • You have a normal six sided cube. I give you six different colors that you can paint each side of the cube with (one color to each side). How many different cubes can you make?Different means that the cubes can not be rotated so that they look the same. This is important! If you give me two cubes and i can rotate them so that they appear identical in color, they are the same cube.

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    • In his final written work, Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), the legendary Italian polymath Galileo Galilei proposed a mathematical paradox based on the relationships between different sets of numbers. On the one hand, he proposed, there are square numbers—like 1, 4, 9, 16, 25, 36, and so on. On the other, there are those numbers that are not squares—like 2, 3, 5, 6, 7, 8, 10, and so on. Put these two groups together, and surely there have to be more numbers in general than there are justsquare numbers—or, to put it another way, the total number of square numbers must be less than the total number of square and non-square numbers together. However, because every positive number has to have a corresponding square and every square number has to have a positive number as its square root, there cannot possibly be more of one than the other.

      Confused? You’re not the only one. In his discussion of his paradox, Galileo was left with no alternative than to conclude that numerical concepts like more, less, or fewer can only be applied to finite sets of numbers, and as there are an infinite number of square and non-square numbers, these concepts simply cannot be used in this context.

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    • Imagine a fletcher (i.e. an arrow-maker) has fired one of his arrows into the air. For the arrow to be considered to be moving, it has to be continually repositioning itself from the place where it is now to any place where it currently isn’t. The Fletcher’s Paradox, however, states that throughout its trajectory the arrow is actually not moving at all. At any given instant of no real duration (in other words, a snapshot in time) during its flight, the arrow cannot move to somewhere it isn’t because there isn’t time for it to do so. And it can’t move to where it is now, because it’s already there. So, for that instant in time, the arrow must be stationary. But because all time is comprised entirely of instants—in every one of which the arrow must also be stationary—then the arrow must in fact be stationary the entire time. Except, of course, it isn’t.

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    • One day, five couples and their children (each couple had only one child) spent the day at an amusement park. They all enjoyed the day tremendously despite the fact that each child managed to get lost at some point during the day. Using the clues and the grids below, determine the full name of each couple, the name and age of each couple’s child, and where each lost child was found.

      1. George, whose last name isn’t Smith, is a good friend of Bill Walker, who is not Susie’s father.
      2. The ages of the children from lowest to highest are the 6 year old, Ann, the one found by the teacups, George’s son, and Jane’s child.
      3. Michael Charming, whose 10-year-old child is the oldest, helped Stan find his daughter, who is a year younger than Ann, by the carousel. Stan’s last name isn’t Smith.
      4. The boy found at the ferris wheel is younger than John but older than Ann. Mary is older than Susie but younger than Tom.
      5. Sally Jackson didn’t find her son at the teacups or the roller coaster. When she looked by the flume, she found Kim’s 7-year-old child.
      6. Al and Linda’s child, who is 8, is the best friend of Michelle’s daughter, who is two years younger.

      Use the grid to help solve the puzzle!

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    • Five bachelors who all lived in the same apartment building each ordered an item from the same catalog. Unfortunately, the shippers got confused and each item was delivered to the wrong apartment. Can you determine each man’s full name, what each man ordered and what was actually delivered, and which apartment each man lived in.

      1. Roger, who doesn’t live in an end apartment, ordered the Television set. Tom lived next door to the man who received the dishware.
      2. Mr. Weiseman, who didn’t receive the automotive tools, lives two apartments from the man who ordered the downhill skis and one apartment from Harry.
      3. Ed, whose last name isn’t Smith, lives in apartment #3 but he didn’t receive the automotive tools. Mr. Smith, who doesn’t live in apartment #4, ordered the golf clubs but he received the item that Mr. Campbell ordered, which wasn’t downhill skis.
      4. The bachelor in apartment #1, which isn’t Tom, ordered what Al received. The man in apartment #2, who didn’t receive the golf clubs, lives next door to where what he ordered was delivered.
      5. Mr. Bates didn’t order the downhill skis. The television set was not delivered to Ed’s apartment.
      6. Tom lives in apartment #5.

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    • Five parents pick-up their children at the Puzzlefry Elementary School every Tuesday to bring the kids to their afterschool activity. Colleen and the four other children all attended a different afterschool activity and their parents always arrive at different times (between 3:00 pm and 3:30 pm). Determine each child’s full name, the first name of the parent picking them up (all the parents’ last names are the same as their child’s), the time each was picked up, and the activity each child is being brought to.

      • Margie’s best friend’s mother, Mrs. Dobson, arrived before Cathy came to pick up her son. Mrs. Walsh picked up her daughter for fencing.
      • Josh Steinway loved football as much as Donno liked chess, and they both liked being the last two to be picked up.
      • David Holden picked up his daughter for her hiking as soon as he could, but Lynne was always there before he was.
      • Margie liked being the first one picked up but she didn’t take ballet or hiking.
      • Lynne’s daughter was not Margie.
      • In order of their departure from school: Ann, the girl who took ballet, Mary Holden, the boy who took football, and Capri Johnson.

      Use the grid to solve the puzzle!

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    • Five friends pooled their resources one day and pieced a CD together from songs they had written. They called their band “The Puzzle Fry”  and ended up playing a number of live gigs at local events. Determine the full name of each band member, the instrument (or mixing console) each played, the brand of equipment each used, plus each member’s favorite magazine.

      • Steve wasn’t the sound engineer. One of the women enjoyed EQ magazine.
      • Angie and Steve didn’t like Recording magazine. The bass player used Ibanez equipment.
      • Mr. Magnus didn’t use Mackie equipment. Mark’s last name wasn’t Hydal and he didn’t play keyboard.
      • The sound engineer, whose last name wasn’t Engel, enjoyed reading Mix magazine. The person who used Yamaha drums wasn’t Robert, but their last name is Hydal.
      • The five band members (in no particular order) were: Mark Scott, the female bass player, the person who read Musician, the one who used Peavey equipment, and Robert.
      • Shelley’s last name was not Hydal or McArthur and she didn’t use Roland equipment. Mackie only developed equipment for live sound and recording NOT musical instruments.
      • Steve McArthur was the guitarist.

      Use the grid to help solve the puzzle!

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    • Imagine you’re holding a postcard in your hand, on one side of which is written, “The statement on the other side of this card is true.” We’ll call that Statement A. Turn the card over, and the opposite side reads, “The statement on the other side of this card is false” (Statement B). Trying to assign any truth to either Statement A or B, however, leads to a paradox: if A is true then B must be as well, but for B to be true, A has to be false. Oppositely, if A is false then B must be false too, which must ultimately make A true.

      Invented by the British logician Philip Jourdain in the early 1900s, the Card Paradox is a simple variation of what is known as a “liar paradox,” in which assigning truth values to statements that purport to be either true or false produces a contradiction. An even more complicated variation of a liar paradox is the next entry on our list.

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