Very Hard Math

Discussion in 'Fun & Games' started by Shawn Hopkins, Apr 1, 2012.

  1. Shawn Hopkins

    Shawn Hopkins TZ Member of the Year 2013

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    Because what's more fun than very hard math? Solve these problems. Show your work.

    A 5 foot-long cylindrical pipe has an inner diameter of 6 feet and an outer diameter of 8 feet.
    If the total surface area is kn(n=Pi) ,what is the value of k ?


    If the number 86 in base ten is represented as 321 in base b, what is the base-ten representation of the number 123 in base b?

    A traveling salesperson shows up at the apartment of a math teacher to peddle her wares. The salesperson discovers that the teacher has 3 children and inquires as to their ages. The teacher answers, The sum of my childrens' ages is 13 the salesperson immediately declares, That's not enough information to deduce your kids ages! the teacher continues,Well the product of their ages is the apartment # The sales person checks for the # thinks for a minute and declares that is still not enough information for me to figure out their ages So the teacher says, Oh i forgot to mention the eldest is allergic to chocolate. At which point the salesperson replies,Aha i know all their ages!!! What are the ages of the children?
     
  2. Jmill

    Jmill Person

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    Answers!

    This is the kind of game that I can play.

    1) Considering the surface area is 2piRH. For the outside of the pipe, R is 4 and H is 5, so SA=40pi. For the inside, R is 3 instead, so the answer is 30pi. Add the two together 30pi+40pi= 70pi. And since SA=kn, where n=pi, you divide the surface area by pi to get your answer: 70! (As in 70, exclamation point, not 70 factorial).

    2) It's obviously 68. You have to reverse the order the numbers come in to get the opposite. Basic geometry.

    3) Since the apartment belongs to a teacher, it is implied that the number must have a educational meaning. Since the three ages must add up to 13, it cannot be a high number. Twelve: the highest grade in the standard American system of education seems like a fit. So X+Y+Z=13 and XYZ=12.

    One can also use the chocolate fact to their advantage. Chocolate is not recommended to be incorporated into a diet until the age of one. Since only the eldest was mentioned, it can be deduced that the eldest is more than one year old, and all children are at least one.

    Finally, by looking at a possible product list, only one adds to thirteen: 11.499999, 1, 1. Adding the three together gives 13.49, which is rounded down. Multiplying forces the first age to 12, creating a product of 12.

    Thus, the solution set is [11.499999, 1, 1].

    Hopefully I didn't defeat the purpose of the thread by solving.
     
  3. Shawn Hopkins

    Shawn Hopkins TZ Member of the Year 2013

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    Ahoy. The last one needs to be whole numbers.
     
  4. Jmill

    Jmill Person

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    -looks over math-

    Oh, how could I forget? Chocolate is the name of her mother's dog! And since the eldest is allergic to dogs, he must be equal to 8.

    And since none of the kids can be the same age, either (a tidbit I picked up from the word choice in the problem), they must equal 3 and 2.

    She lives in Apartment 48, and her kids are [2,3,8].
     
  5. Shawn Hopkins

    Shawn Hopkins TZ Member of the Year 2013

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    Ahoy. The answer I got was 9,2,2. The chocolate allergy is a red herring, the point is that oldest isn't a twin.

    http://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.95189.html
     
  6. Jmill

    Jmill Person

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    Ah, that makes sense.
     
  7. Aquadementia

    Aquadementia That's a lot of Mulaney!

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    1: I took a more direct approach of twice the average diameter times length, so 70.

    2: It's a base 5 number, get that by dividing by the first digit, 3, then looking at the nearest perfect square. Then check. And it checked out, so the number you're looking for is 38.

    3: I couldn't get and it wasn't until I looked at the answer that I realized which piece of information I didn't include. By which I mean taking into account that the salesman actually was doing his math correctly. It's only then that you would look for numbers that are not unique. That's not something I'd take for granted.
     

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