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(OT) Math Puzzle (from Bean in 2005) — Parallax Forums

(OT) Math Puzzle (from Bean in 2005)

doggiedocdoggiedoc Posts: 2,246
edited 2011-03-30 13:18 in General Discussion
Bean you never gave the answer:
Bean wrote: »
This one is not a trick, it will make you think though.

A man is floating in a boat in a pool. There is also a large stone in the boat.
The man pushes the stone out of the boat and the stone sinks to the bottom of the pool.
Does the water level in the pool go up, down or stay the same (as when the stone was in the boat).

See if you can figure it out BEFORE you google it...

Bean.

Original Post here.

Paul
«1

Comments

  • doggiedocdoggiedoc Posts: 2,246
    edited 2011-03-25 19:44
    My proposed answer from then:
    doggiedoc wrote: »
    Bean - I say it depends on the size of the stone. The stone's displacement while in the boat is based on it's weight and the surface area of the boat. The heavier the stone the more water it displaces. When the stone is dropped overboard into the water; how much water it displaces is determined by the stone's volume. Therefore it depends on the density of the stone as to whether the water level goes up or down or stays the same.

    I think.

    Doc
  • Erik FriesenErik Friesen Posts: 1,071
    edited 2011-03-26 10:45
    If the rock sinks, the water level will go down. When the pool lining cracks it will go down further.
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-03-26 11:20
    The fact that the stone sinks means that it displaces more water by weight than by volume, so the water level will go down.

    -Phil
  • ercoerco Posts: 20,260
    edited 2011-03-26 13:55
    Down, since the weight of the rock is now borne by the pool bottom, and not pushing the boat down into the water and driving the water level up. As long as it sinks, its density is greater than water, so its volume displacement is less than the volume of its equivalent weight in water. Simple deductive reasoning, my dear Watson.

    But if you like a good math problem and similar triangles, try http://en.wikipedia.org/wiki/Crossed_Ladders_Problem
  • HollyMinkowskiHollyMinkowski Posts: 1,398
    edited 2011-03-26 14:07
    Eureka! :-)

    Yes, the level would go down.

    If the guy stood up and peed over the side would the water level change? LoL
    (might this be very slightly dependent upon the temp of the water vs the pee?)
  • ercoerco Posts: 20,260
    edited 2011-03-26 14:25
    So Holly the MODERATOR has 2 bathroom humor posts with the words pee and wee it them. Anything goes! It's THUNDERDOME around here. It's dogs sleeping with cats! :)
  • HollyMinkowskiHollyMinkowski Posts: 1,398
    edited 2011-03-26 14:36
    Speaking of dogs sleeping with cats...

    There is a farmer in China claiming one of his sheep gave
    birth to a puppy :-)

    images?q=tbn:ANd9GcQbCLZBgar5I9e03LvFsDYOjQVgGltOkd3B7VVG5KRtZsVQaBMR3w

    Anyways...I only became a moderator because I am
    often on the forum when many in the US are asleep.
    So I can delete those spam Viagara posts in the WEE hours....LoL
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-03-26 14:39
    HollyMinkowski wrote:
    There is a farmer in China claiming one of his sheep gave birth to a puppy
    'Kinda gives new meaning to the word "mutton", doesn't it?

    -Phil
  • Martin_HMartin_H Posts: 4,051
    edited 2011-03-26 15:13
    Erco just nerd sniped* me with that ladder question.

    * See XKCD http://xkcd.com/356/
  • K2K2 Posts: 693
    edited 2011-03-26 15:15
    HollyMinkowski wrote: »
    Speaking of dogs sleeping with cats...

    There is a farmer in China claiming one of his sheep gave
    birth to a puppy :-)

    That's no big deal. My aunt has had a sheepdog for years.
  • HollyMinkowskiHollyMinkowski Posts: 1,398
    edited 2011-03-26 15:28
    nerd_sniping.png
  • ercoerco Posts: 20,260
    edited 2011-03-26 15:56
    Further, there are 2 men standing with the ladders one always tells the truth and the other always lies. You don't know which is which. You can ask only one question to one man...
  • HollyMinkowskiHollyMinkowski Posts: 1,398
    edited 2011-03-26 17:07
    erco, huh?

    You mean how do you discern which is the liar and which is truthful?

    You could ask either of them any question where the answer is
    obvious.

    Are you a man?
    Is that a ladder?
    Is the sky blue?

    I have to be missing something here???

    I looked at that ladder question, it made my head hurt.
  • ercoerco Posts: 20,260
    edited 2011-03-26 17:15
    Holly: There is no ladder.
  • HollyMinkowskiHollyMinkowski Posts: 1,398
    edited 2011-03-26 17:22
    erco wrote: »
    Holly: There is no ladder.

    Now my head hurts again.
  • TtailspinTtailspin Posts: 1,326
    edited 2011-03-26 18:35
    Err,. Um... What is the equivalent resistance between the two marked nodes??:nerd:
  • doggiedocdoggiedoc Posts: 2,246
    edited 2011-03-26 18:38
    Phil Pilgrim (PhiPi) wrote: »
    'Kinda gives new meaning to the word "mutton", doesn't it?

    -Phil

    Good one Phil!
  • doggiedocdoggiedoc Posts: 2,246
    edited 2011-03-26 18:39
    K2 wrote: »
    That's no big deal. My aunt has had a sheepdog for years.

    Another good one!!
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-03-26 18:40
    Ttailspin wrote:
    Err,. Um... What is the equivalent resistance between the two marked nodes??
    If you're a rook, a king, or a queen, it's 2; a knight, 1; a bishop, infinity.

    -Phil
  • TtailspinTtailspin Posts: 1,326
    edited 2011-03-26 20:04
    So Holly, what are You taking for the head aches? I am gonna need some...
    Thanks to Phil..
    If you're a rook, a king, or a queen, it's 2; a knight, 1; a bishop, infinity.
  • Beau SchwabeBeau Schwabe Posts: 6,568
    edited 2011-03-26 22:20
    "A man is floating in a boat in a pool." ... wouldn't the boat be floating and not the man? Do we know for sure that the boat is floating or is it just the man?

    If the man is dead floating in a sunk boat then there is nobody to move the rock... the water level stays the same. :-)
  • HollyMinkowskiHollyMinkowski Posts: 1,398
    edited 2011-03-26 22:43
    @tailspin
    I never get headaches any more, my OCD meds killed them off.

    That question and similar brain teasers give me a pain no medication
    could stop....well, perhaps a roofie might ;-)

    @Beau Schwabe
    You are thinking far afield! Angling way way out there on obscure tangents.
    I bet you play chess huh? I gave up chess, it brings on those head
    pains too...LoL All I play now is practical jokes.... I'm the queen of
    practical jokes.... the funny stories I could relate :-)
  • doggiedocdoggiedoc Posts: 2,246
    edited 2011-03-27 04:58
    Beau Schwabe (Parallax) wrote: »
    "A man is floating in a boat in a pool." ... wouldn't the boat be floating and not the man? Do we know for sure that the boat is floating or is it just the man?

    If the man is dead floating in a sunk boat then there is nobody to move the rock... the water level stays the same. :-)

    Excellent point Beau! I think Bean needs to clarify the question!

    Paul
  • BeanBean Posts: 8,129
    edited 2011-03-27 06:29
    Beau, You are such a trouble-maker...

    What if the pool was floating inside a bigger pool. Would the water level change in the bigger pool ?

    Bean
  • TtailspinTtailspin Posts: 1,326
    edited 2011-03-27 07:01
    One would want to ensure that any Tidal influences are accounted for.. it could be as much as thirty feet,
    or more in some cases.

    Maybe check the local Surf Report too.. thats allways a good idea anyway before starting a major project...
  • Beau SchwabeBeau Schwabe Posts: 6,568
    edited 2011-03-27 07:23
    HollyMinkowski,
    "You are thinking far afield! Angling way way out there on obscure tangents." - Just keeping true to my style :-)

    "I bet you play chess huh?" - Poker instead


    Bean,
    "You are such a trouble-maker..." - I wouldn't have it any other way :-)

    "What if the pool was floating inside a bigger pool. Would the water level change in the bigger pool ?" - A pool floating on another pool ... sounds like oil and water ... no, the bigger pool in this case would not change it's level.

    On the first problem though... it boils down to displacement by weight verses displacement by volume. If the rock is in the boat (assuming that the boat IS floating) the water is displaced by weight, but by being in the boat the weight is dispersed evenly across the area of the boat in contact with the water.... As far as it's concerned, the water "sees' the man+boat+rock as a lower density object than itself so all of it floats within the boat. If the rock is thrown over, then depending on the size of the rock, the the volume will displace the water a certain amount, The question is, Is the displacement by weight (man+boat) greater or less than the displacement by volume of just the rock in the water. If the volume is greater, then the water level will go up, if the displacement by weight is greater, the water level will go down. If they are equal then there will be no change.

    For this problem, I don't think there is enough information, since the effective weight displacement can be governed by the size of the boat, and density of the rock.
  • Dave HeinDave Hein Posts: 6,347
    edited 2011-03-27 08:09
    What if the stone was a large chunk of salt. The water level would continue to lower as the salt dissolved into the water. Not only that, but the boat would rise higher up in the water because of the increased density of the water, which means the water level would be even lower.
  • sam_sam_samsam_sam_sam Posts: 2,286
    edited 2011-03-27 08:12
    Bean wrote: »
    What if the pool was floating inside a bigger pool. Would the water level change in the bigger pool ?

    Bean

    You my head hurt this to funny to think about
  • sam_sam_samsam_sam_sam Posts: 2,286
    edited 2011-03-27 08:14
    Dave Hein wrote: »
    What if the stone was a large chunk of salt. The water level would continue to lower as the salt dissolved into the water. Not only that, but the boat would rise higher up in the water because of the increased density of the water, which means the water level would be even lower.

    You are both making my head hurt even more

    Beau Schwabe

    "You are such a trouble-maker..." - I wouldn't have it any other way :-)

    "What if the pool was floating inside a bigger pool. Would the water level change in the bigger pool ?" - A pool floating on another pool ... sounds like oil and water ... no, the bigger pool in this case would not change it's level.

    On the first problem though... it boils down to displacement by weight verses displacement by volume. If the rock is in the boat (assuming that the boat IS floating) the water is displaced by weight, but by being in the boat the weight is dispersed evenly across the area of the boat in contact with the water.... As far as it's concerned, the water "sees' the man+boat+rock as a lower density object than itself so all of it floats within the boat. If the rock is thrown over, then depending on the size of the rock, the the volume will displace the water a certain amount, The question is, Is the displacement by weight (man+boat) greater or less than the displacement by volume of just the rock in the water. If the volume is greater, then the water level will go up, if the displacement by weight is greater, the water level will go down. If they are equal then there will be no change.

    For this problem, I don't think there is enough information, since the effective weight displacement can be governed by the size of the boat, and density of the rock.
  • Beau SchwabeBeau Schwabe Posts: 6,568
    edited 2011-03-27 08:32
    My oldest daughter and I just did an experiment: and we have our answer. :-)

    1 six inch plastic bowl filled 1/2 way with water = Pool
    ALTOIDS Box (remove lid) = Boat
    1/4 1/3 measuring cup = Man
    10 marbles = rock used in test #1
    15 quarters = rock used in test #2
    Electrical tape = used to mark the levels on the plastic bowl ... and cover the holes on the ALTIODS Box where the lid attached.

    Note: The 1/4 1/3 measuring cup was to keep the center of weight in the 'boat', otherwise the marbles would roll to one corner and sink the boat.
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