Thursday, November 15, 2007

Solution: Legs in the Bus?

There are a lot of legs on this bus!
Last week, I posted the Legs in the Bus brainteaser. It's a pretty challenging math problem; it is not a trick question. Some people got it right (David after a couple of attempts, Anali, and Karen ) and others - who will remain nameless - didn't even come close.



There are a lot of cats in this backpack!
  • There are 7 girls on a bus

  • Each girl has 7 backpacks

  • In each backpack, there are 7 big cats

  • For every big cat there are 7 little cats


  • So how many legs are there in the bus?





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    plezWorld Solution

  • There are 7 girls on a bus

  • Each girl has 7 backpacks

  • In each backpack, there are 7 big cats: 7 girls x 7 backpacks/girl x 7 big cats/backpack = 343 big cats

  • For every big cat there are 7 little cats: 7 girls x 7 backpacks/girl x 7 big cats/backpack x 7 little cats/big cat = 2401 little cats

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  • 7 girls x 2 legs/girl = 14 girl legs

  • 343 big cats x 4 legs/cat = 1372 big cat legs

  • 2401 little cats x 4 legs/cat = 9604 little cat legs

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  • 14 girl legs + 1372 big cat legs + 9604 little cat legs = 10,990 legs



  • There are 10,990 legs in the bus


    16 comments:

    Anali said...

    Yipeee!!! I won! I won! ; )

    David Sullivan said...

    That brain teaser was like my golf game, if I get a second(or third chance) I can always get a par, or in this case a win (ok, tie)

    plez... said...

    as the group Chocolate Milk once sang, "Everyone's a winner, baby, and that's the truth..."

    shade said...

    well i think the questions is not very clearly stated. It does use ambigous words like "in the bus" and doesn't specify that kittens also have 4 legs or whether there was a bus driver etc. Plus, some bus chairs would also have legs...so the Question is not very clear which makes the answer so much more difficult if you expect it that way :) But it seems the answer it's pretty straignt forward as long as you remember to add the cats and kittens groups. It helps if you do it methodically, step by step and visualise/draw the groups :)

    plez... said...

    shade,

    what is ambiguous about "in the bus"? the brainteaser asks how many total legs are in the bus... i don't see the ambiguity there.

    ...and unless the kitten (small cat) is deformed, it will have four legs.

    ...and there was no mention of a bus driver, so why would that even come into play?

    ...and there was no mention of the bus chairs, so why be concerned about that?

    you can only answer a problem (any problem) with the information that is provided to you: 7 girls, 7 backpacksper girl, 7 big cats per backpack, and 7 little cats for every big cat!

    Copacetic said...

    The riddle states that there are seven little cats per each big cat, seven big cats per bag, and each girl has seven bags -- it never states that the bags are ON (or, in this case IN) the bus.

    The answer is 14.

    Kaitie said...

    I am a seventh grader and I found the answer to this problem with no help and two pieces of paper. My grandfather, on the other hand, who has a degree in math could not find the answer to this problem correctly. It only comes to show that the answer to this problem can only be found with creativity, not just math skills! ^_^

    plez... said...

    kaitie,

    good job! the problem is only difficult if you choose to make it difficult... thanks for stopping by to share you wisdom!

    bob b. blue said...

    Your answer is wrong.

    You incorrectly multiplied the number of girls into the formula.

    The correct answer is 1582 legs in the bus.

    The number of legs are:

    14 girls legs. (14x2)
    196 big cat legs. (7x7x4)
    1,372 small cat legs. (7x7x7x4)

    Add them up to 1,582.

    bob b. blue said...

    In haste my last post was wrong.
    I have corrected the girls legs formula to (7x2)

    =====================

    Your answer is wrong.

    You incorrectly multiplied the number of girls into the formula.

    The correct answer is 1582 legs in the bus.

    The number of legs are:

    14 girls legs. (7x2)
    196 big cat legs. (7x7x4)
    1,372 small cat legs. (7x7x7x4)

    Add them up to 1,582.

    plez... said...

    bob b.,

    in your haste to prove me wrong... you missed ONE important fact, each girl was carrying 7 backpacks which each had 7 big cats: 7x7x7x4 = 1372 big cat legs.

    and then there were 7 little cats for each big cat: 7x7x7x7x4 = 9604 little cat legs.

    after you add ALL those legs up, you end up with 10,990 legs in total (the answer that i provided in the solution)!

    Chad said...

    This is how I got it

    7 girls x 7 backpacks = 49

    7 big cats x 49 backapacks = 343

    343 big cats x 7 little cats = 2401 numbaer of little cats

    2401 little cats + 343 big cats = 2744 total cats

    2744 cats x 4 legs = 10976 total cat legs

    10976 total cat legs + 14 girl leag = 10990 total legs


    10990 total legs

    VolteFace said...

    The bus driver has no-legs!!!!!
    sorry for the guy :(

    :)

    Lou said...

    Ok, I admit that I also got 1582 and understand that I was wrong. But really, how many fifth graders actually get that right? I would guess very few and would like to see the statistics.

    The absurdity of it is also distracting and leads to a web of thoughts that go from "Why?" to "That many girls, cats and bags could never fit on a bus.

    So the smartest/fastest way to get to the correct answer is, GOOGLE the question and voila! the correct answer magically appears! Now what really is the world coming to...;( That is what a smart fifth grader would have done.

    In fact, I was in a training program where we were presented with a similar problem and one team that had a member with a Blackberry found the answer to a "Stack the Nail" puzzle to solve the team building exercise in virtually no time at all. So it goes to show that 1 industrious person can likely outperform a team any day.

    Excelsior!

    Partymonster said...

    Plez, the band was "Hot Chocolate". Their biggest hit was "You Sexy Thing"

    brittany said...

    It took me a week to figure out this problem i tried and tired the sad thing is im in 9th grade and i even asked my math teacher she said it should be the bus doesnt have legs it has wheels so when i found the answer on here i was happy.