Bad Dog brain teaser!

Discussion in 'Bad Dog Cafe' started by Junkyard Dog, Mar 13, 2019.

  1. Lake Placid Blue

    Lake Placid Blue Poster Extraordinaire

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    So...... Chunks was right. 2 and a bit.
     
  2. rcole_sooner

    rcole_sooner Poster Extraordinaire Silver Supporter

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    I'm guessing the messenger travels twice as fast as the column, and travels 1.5 times the length of the column.

    I didn't do any math, just shot from the hip.
     
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  3. Junkyard Dog

    Junkyard Dog Tele-Afflicted

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    The pace of the messenger is not given...nor is the pace of the troops. It can be solved without knowing them...see my solution a few posts back for explanation.
     
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  4. Junkyard Dog

    Junkyard Dog Tele-Afflicted

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    He was close. A bit is 0.125. So not a bad guess...only off by a third of a mile. ;)
     
  5. rcole_sooner

    rcole_sooner Poster Extraordinaire Silver Supporter

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    Yep, I reread and got that. Word problems always got me in math. :lol:
     
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  6. Steve 78

    Steve 78 Tele-Afflicted

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    I see Junkyard Dog has already posted it, but I finally got it this morning as well (I think in a slightly different way).

    So at the start the messenger is a mile in front of the end of the column and a mile behind his final position. The actual speed doesn't really matter but the ratio of the speeds of the column and messenger does. So I will say the column is walking at 1 mph and the speed of the messenger will be 1 x (ratio of speeds). If the column is walking at 1 mph the total time will be 1 hour. So the distance the messenger travels will also equal his speed (as he is also traveling at a constant speed for 1 hour).

    Let's call the point where the messenger reaches the end of the column before he turns around 'x'. He travels there, then back to his original position, then 1 more mile. So his total distance is 2x + 1. This is also his speed (2x + 1 mph).

    The column is traveling at 1 mph. Let's call the messenger's speed 's' for now. The distance traveled by the end of the column and the messenger will add up to 1 as there is 1 mile between them at the start. Depending on the messengers speed, where they meet can vary. The end of the column will have traveled 1/(s+1) and the messenger will have traveled s/(s+1) - these are the ratios of their speeds which add up to 1. (I messed up this part, several times, originally).

    We have established speed and distance are the same so

    x = s/(s +1)
    x = (2x + 1)/(2x+1 +1)
    x(2x+2) = 2x +1
    2x^2 + 2x = 2x + 1
    2x^2 - 1 = 0
    x^2 - 1/2 = 0
    difference of squares rule
    (x + sqrt[1/2])(x - sqrt[1/2]) = 0
    x = sqrt(1/2)
    total distance = 2x + 1
    = 2 * sqrt(1/2) + 1
    = 2.4142 miles

    Nice one Junkyard Dog (and Hoodie!), although I would call this an advanced high-school maths problem more than a brain teaser :D
     
  7. Steve 78

    Steve 78 Tele-Afflicted

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    Here's a brain teaser. Fred builds his house so that all of the walls are facing south. One day he is looking out his window and sees a bear. What colour is the bear?
     
  8. 24 track

    24 track Doctor of Teleocity Silver Supporter

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    ice cream has no bones?
     
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  9. 24 track

    24 track Doctor of Teleocity Silver Supporter

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    actually you are all wrong with the answer , the guy stood there untill the back of the line caught up then ran back to the front so....... 1 mile
     
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  10. Steve 78

    Steve 78 Tele-Afflicted

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    Think about it :)
     
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  11. Steve 78

    Steve 78 Tele-Afflicted

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    It's a good answer except that the problem states he is moving at a constant speed. Still, you could argue that he is, but just takes his time to get going ;)
     
  12. Boubou

    Boubou Doctor of Teleocity Gold Supporter

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    I used to love and be good st these problems, right now it’s giving me a headache . I would need to sit down with pen and paper.
    Here is a random page from my quantum mechanics book, yes I understood it all, sigh.
    531128D1-DBFF-4887-80B5-6AC8935BD438.jpeg
     
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  13. Paul in Colorado

    Paul in Colorado Telefied Ad Free Member

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    But how long did he spend telling the guys in the back the orders from the front? And wouldn't he be walking while he did as the troops were moving?
     
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  14. Lake Placid Blue

    Lake Placid Blue Poster Extraordinaire

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    White
     
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  15. Jupiter

    Jupiter Telefied Silver Supporter

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    And don’t forget it takes time to turn around!
     
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  16. boneyguy

    boneyguy Doctor of Teleocity

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    That's how I translate what you said.

    No wonder I didn't figure it out.....there's actual mathematical thinking involved!!!
     
  17. HoodieMcFoodie

    HoodieMcFoodie Doctor of Teleocity Ad Free Member

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    The bear is white. The house is at the north pole.
     
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  18. HoodieMcFoodie

    HoodieMcFoodie Doctor of Teleocity Ad Free Member

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    He didn't tell anyone anything. He delivered a message on a piece of paper. Hand it over and get going.
     
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  19. Lake Placid Blue

    Lake Placid Blue Poster Extraordinaire

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    Maybe the recipient of the message couldn’t read. So the messenger had to read it to him. Maybe the OP misspelled “massage.” Some massages take a long time. Some go quick. I think we need more info.
     
  20. SecretSquirrel

    SecretSquirrel Tele-Afflicted Ad Free Member

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    This is why I didn't become an astronomer. :oops:
     
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