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Brain Teasers (Starting with the Monty Hall Problem)

Discussion in 'Fred's House of Pancakes' started by stevepea, Aug 24, 2020.

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  1. stevepea

    stevepea Senior Member

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    Brain Teasers... Feel Free to add your own Brain Teaser here!

    I have a friend who can't wrap his head around this: if you roll a die once, (assuming it's not defective), the chance of you getting a "3" is.... 1 in 6. But say you roll it 10 times -- and EACH of the 10 times it just happens to land on a "3" each time (again, assume it's just by chance, not because of any defect)... Question: What are the chances of rolling a "3" on your next try, which would make it 11 times in a row? The answer is still... 1 in 6.

    But here's one I like better. Those who know statistics & probability (not me) certainly already know this, but for those out there who don't and like a good brain teaser...

    Say you go back in time to the 1970s and go on the game show "Let's Make a Deal" -- where there are 3 closed doors ("Door 1" "Door 2" & "Door 3"), and behind one of them is a brand new car -- but behind the other two are goats (baaa!) The host (Monty Hall) knows which door the car is behind, but you (of course) don't. To win the car, you have to pick the correct door where the car is behind.

    At the start of the game, you have a 1 in 3 chance of picking the right door (since there are 3 doors, all shut).

    You're first asked to pick a door (which will remain sealed and not opened yet).
    Say.... you choose "Door #1"

    The host will then open up one of the REMAINING doors (Say he opens up... Door #2) and there's a goat in there.

    So.... you have two doors left where the car could be: (in this case, either Door #1 or Door #3, with both still being shut).

    Question: When Monty then asks "Do you want to stay with your initial choice of Door #1, or switch to Door #3?", what should you do? Would it make any difference at all?

    Here's a quick YouTube on the answer:


     
    #1 stevepea, Aug 24, 2020
  2. bisco

    bisco cookie crumbler

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    without watching the video, i'm going to guess no
     
    #2 bisco, Aug 24, 2020
  3. ChapmanF

    ChapmanF Senior Member

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    Without watching the video, I'll figure ... there's a 1/3 chance you've already picked the car, and will win it by keeping the door you picked first.

    There's a 2/3 chance that you haven't picked the car yet, but now know what door it's behind.
     
    #3 ChapmanF, Aug 24, 2020
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  4. RRxing

    RRxing Senior Member

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    What makes this number unique - 8,549,176,320?
     
    #4 RRxing, Aug 24, 2020
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  5. RRxing

    RRxing Senior Member

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    A sundial has the fewest moving parts of any timepiece. Which has the most?
     
    #5 RRxing, Aug 24, 2020
  6. Prius Maximus

    Prius Maximus Senior Member

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    An electric train is rolling down the tracks at 80 mph southward (180 degrees from north). The wind is blowing east at 20 mph (90 degrees from north). What numerical direction and speed does the smoke go?
     
    #6 Prius Maximus, Aug 24, 2020
  7. ChapmanF

    ChapmanF Senior Member

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    The smoke goes south (180 degrees) at 80 mph, because it's trapped inside the electronics compartment, moving with the train.
     
    #7 ChapmanF, Aug 24, 2020
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  8. Raytheeagle

    Raytheeagle Senior Member

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    Alphabetical order(y).
     
    #8 Raytheeagle, Aug 24, 2020
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  9. hill

    hill High Fiber Member

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    What is the only man-made thing in heaven.
    .
     
    #9 hill, Aug 24, 2020
  10. TMR-JWAP

    TMR-JWAP Senior Member

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    I've always liked this one, just for the simplicity..........
     
    #10 TMR-JWAP, Aug 24, 2020
  11. fuzzy1

    fuzzy1 Senior Member

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    You don't remember any of the multiple times this puzzle has previously gone around during your lifetime?
     
    #11 fuzzy1, Aug 24, 2020
  12. fuzzy1

    fuzzy1 Senior Member

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    (1) Which is heavier, an ounce of gold, or an ounce of feathers?

    (2) Which is heavier, a pound of gold, or a pound of feathers?

    [Hint: if you get the same answer for both, you missed the trick.]
     
    #12 fuzzy1, Aug 24, 2020
  13. GabrielD

    GabrielD Member

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    Electric train does not have smoke...
     
    #13 GabrielD, Aug 24, 2020
  14. GabrielD

    GabrielD Member

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    A snail falls into a 10 meter deep fountain, he wants to get out, he does the following. The day goes up 3 meters and the night goes down 2 meters. How many days does the snail need to reach the surface?
     
    #14 GabrielD, Aug 24, 2020
  15. Mendel Leisk

    Mendel Leisk Senior Member

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    Ten??
     
    #15 Mendel Leisk, Aug 25, 2020
  16. GabrielD

    GabrielD Member

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    No, sorry

    Normally, he gains 1 meter by day...
    After 7 days the snail is at 7 meters, next day will go up 3 meters, and there is it... Answer = 8 days
     
    #16 GabrielD, Aug 25, 2020
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  17. Mendel Leisk

    Mendel Leisk Senior Member

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    Ahh
     
    #17 Mendel Leisk, Aug 25, 2020
  18. Mark57

    Mark57 2021 Tesla Model 3 LR AWD

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    Spock, how do you feel?
     
    #18 Mark57, Aug 25, 2020
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  19. GabrielD

    GabrielD Member

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    A water lily on a lake has the ability to grow in such a way as to double its surface every day. If in 30 days the whole lake is occupied by the water lily, in how many days will half of the lake be occupied?
     
    #19 GabrielD, Aug 26, 2020
  20. RRxing

    RRxing Senior Member

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    #20 RRxing, Aug 26, 2020
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