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Thread: Mathman (and others) -- see if you can solve this one!

  1. #1
    Ptichka
    Guest

    Mathman (and others) -- see if you can solve this one!


    OK, guys, here is probably my all time favorite math puzzle.

    Bob and Sam meet on the street. They have not seen each other for many years.
    Bob: Hey, long time no see! How have you been?
    Sam: Fine
    Bob: Any kids?
    Sam: Yes, three
    Bob: What ages?
    Sam: Well, you always liked puzzles, so let me tell you this. The product of their ages is 36, and the sum is equal to the number of windows in the house across the street.
    Bob (after thinking a while): That is not enough.
    Sam: You are right. Here is one more piece of info: the oldest has red hair.
    Bob: Ahhh, now I know!

    What are the ages of of Sam's kids?

    BTW, yes, there is an answer to this puzzle. The only assumption you need to make is that when Bob says he does not have enough info, indeed there is not enough info at that point to determine the kids' ages. And that when Bob says he knows, he indeed does know.

    So, any takers?

  2. #2
    emiC
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    I have no answer but I can start by dividing 36 into prime numbers

    3 / 3/ 2/2/1

    and look at the possible combos

    9 X 4 X 1 = 36, sum = 14
    9 X 2 X 2 = 36, sum = 13
    18 X 2 X 1 = 36, sum = 21
    3 X 6 X 2 = 36, sum = 11
    3 X 3 X 4 = 36, sum = 10
    3 X 12 X 1 = 36, sum = 16
    6 X 6 X 1 = 36, sum =13

    I am sure there are more. So someone take it from here?:lol:

    We are a team here at GS.

    PS, if there is a prize e.g. a virtual plate of dim sum, I get first pickings.:rollin:


  3. #3
    DrWatson
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    My heartiest gratitude, Ms. emiC, for doing all the work for me. From here it's "elementary":

    Sam has a red-headed nine-year-old and a pair of two-year-old twins.

    Hoping to find both of my friends Ptichka and emiC in good health and good spirits, I am

    humbly yours,

    John Watson, M.D.

  4. #4
    emiC
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    <blockquote><strong><em>Quote:</em></strong><hr>the oldest has red hair.[/quote]

    You said the oldest, not "older ones" or "older one"

    That means all 3 kids have different ages? \we can eliminate a few possibilities, and the following are left:

    9 X 4 X 1 = 36, sum = 14
    18 X 2 X 1 = 36, sum = 21
    3 X 6 X 2 = 36, sum = 11
    3 X 12 X 1 = 36, sum = 16

    PS, that is so different from Dr. Watson's answer, why?



  5. #5
    DrWatson
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    Even if the "oldest" is not a twin, the younger two could be. The nine-year-old is even so the "oldest of the three."

    Hint: Look at it from Bob's point of view. He knows, even if we don't, how many windows are in the house across the street.:lol: (Well done, Mr., Ms. or Dr. Ptichka!)

    J.W.

  6. #6
    eltamina
    Guest

    We are doing virtual prize here?


    For a virtual bowl of these candies:

    Our mystery composer had the same name as this brand of candy. (3 letter word)

    The name of the mystery composer and delicious candy is ---


    Hint: one was born in Austria, the other in Germany


  7. #7
    Ptichka
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    Good job Dr. Watson!

  8. #8
    mathman444
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    Darn, I'm late again!

    Ptichka's problem, as shown in emiC's analysis above, is about adding together various factors of 36. The factors of 36, not counting 36 itself, are

    1,2,3,4,6,9,12 and 18.

    If you add these all up you get

    1+2+3+4+6+9+12+18 = 55 (much bigger than 36)

    On the other hand, if we try 38, the only proper factors are 1 and 19, and

    1+19 = 20 (<em>less</em> than 38 )

    Are there any numbers N for which the proper factors all add up exactly to the number itself?

    Yes! N = 6. The proper factors are 1, 2 and 3, and 1+2+3 = 6. (Ya-ay!)

    I also found N = 28:

    1+2+4+7+14 = 28.

    Can anyone find two more?

    Mathman

    PS. I'm still working on the candy. Is it Goodnplenty? I know that Hector Goodnplenty wrote a well known oboe concerto. Oh, no. Too many letters.

  9. #9
    sk8cynic
    Guest

    Mystery Composer


    Elta,

    Are you going by his first or last name? I'm assuming last name but want to be sure.

  10. #10
    Freddy the Pig 2
    Guest

    Re: Mystery Composer


    Hey, Eltamina. I'm good at stuff like this. Just give me a chance here....a three-letter name?...OK, here I go...

    Sir Arnold Bax (1883-1953). Probably an Anglization of "Bach," don't you think? I couldn't find any candy named Bax, but here are some candy <em>dishes</em> with that name. Does that count?

    www.wholesale-glass-deale.../page3.htm

    Tan Dun (1957-- ). Here is a dun foal named Candy:

    www.copperascreek.com/More98foals.html

    John Gay (1685-1732). Well, I found a web site called "Gay Candy" -- does that count? (URL omitted, LOL.)

    Fernando Sor (1778-1839). Here's the premier sor candy site. Oh wait, that's <em>sour</em> candy. Never mind.

    www.zours.com/be_a_zip_flash.html

    Joseph Suk (1874-1935). <em>Candy</em> Lo and Cheung <em>Suk</em>-ping were both nominated for the Hong Kong film awards!

    www.lovehkfilm.com/featur...a_2000.htm

    Wait, don't click me off! All this is leading up to...

    <span style="color:red;font-size:medium;">Johann Christoph Pez (1664-1716)</span>

    www.kdfc.com/new/composer...cfm?id=295

    Do I win a prize? My favorite skater is Michelle Kwan. Her birthday is July 7th. I think she should get a full set of "Disney-with-attitude" Pez dispensers as a birthday gift from Golden Skate.

    www.spectrumnet.com/pez/s...ml#extreme

    Freddy

  11. #11
    eltamina
    Guest

    Re: Mystery Composer


    Cyn I mean last name. What was your answer?

    Freddy congrats, Pez is the answer, or at least the answer I have in my mind.

    The candy was born in Austria, and the composer was born in Munich.

    Sure Michelle will receive a gift for her birthday, I am deciding among WAM's mass in C minor, Felix Mendelssohn Bartholdy's oratorio Elijah, or Tallis Spem in Alium j/k :rollin:

    Freddy, you don't even know that she loves junior mints?

    So no candy dispenser for her, it will look so odd to dispense junior mints from a Pez dispenser.

    I think I will send her the same set of cds I sent Tara. (You know as a dual fan, I have to balance things out).

    So Freddy, which address shall I send the cds to? I assume you will write a poem for the occasion?

  12. #12
    eltamina
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    MM said, "On the other hand, if we try 38, the only proper factors are 1 and 19, and
    1+19 = 20 (less than 38 ) "

    Huh? 1X2X19 = 38, and sum = 22?

    BTW for those of us who struggled so much in math, care to define what is a proper factor?



  13. #13
    Ptichka
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


    Mathman,
    the other numbers are <strong>496</strong> and <strong>8128</strong>.

    Come on, give us something we can actually <em>think</em> about, not just write a computer program to solve!

  14. #14
    eltamina
    Guest

    MM


    Was I correct with the 1 + 2 +19?

    If I am right, I am claiming a prize from you. it won't cost you a dime. :rollin:

  15. #15
    mathman444
    Guest

    Re: Mathman (and others) -- see if you can solve this one!


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