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rocdocmac

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Posts posted by rocdocmac


  1. The probability that any one person selected at random was born on a Wednesday, is 0.1429 (~14 %).

     

    What is the probability that of any …

    (1)   Seven persons chosen at random, exactly one was born on a Friday?

    (2)   Five persons chosen at random, three were born on a Sunday?

     

    [Mr Moderator, if this question has appeared before, please remove it!]

     

     

     

     


  2. 34 minutes ago, Thalia said:

     

    34 minutes ago, Thalia said:

    Think I found one of the 2 I changed from correct to incorrect. But I think that would leave one of these as still wrong though I can't figure out which. . .

      Hide contents
    MMM (2) 5.11.23 5.11.15        
    CCC (3) 1.3.7 1.3.27 1.9.21      
    CCX (3) 1.3.14 1.9.14 1.14.27      
    CEX (4) 1.2.14 1.6.14 1.8.14 1.14.18    
    CMX (2) 1.5.14 5.14.21        
                 
    EMX (3) 2.5.14 5.12.14 5.14.20      
    MMX (2) 5.11.14 5.14.23        
    Spoiler

    Yes, you have indeed found one of them!

    Have another look at XCE and XEE. If you add the other two newly combinations found by you, you will have at least 10/16 correct.

    Hope it helps!

    We can later deal with the more difficult ones!

     

     

     


  3. Spoiler

    The general formula for the volume of an even-dimensional n-sphere is ...

    image.png.76bae2a98a068993e688d83c54f5c98b.png

    After the maximum unit volume in D7 is reached, the ratio starts dropping sinceimage.png.ac4d3df9fd492f64d56afecc68a4f47c.png grows much faster than image.png.dc0c9549207923548a0c9fee4293a692.png.

    So by the time you reach n=1000 (or higher towards infinity), the value for the numerator cannot compete with that of the denominator at all and therefore a second maximum cannot occur.

     


  4. 13 hours ago, Molly Mae said:

    Anyway, I don't think this deserves a spoiler.  Lying can refer to placing oneself in a horizontal position, but it is also the act of being untruthful.  Incidentally, I can find no evidence that "lieing" is an English word.

    Oops, you're right! Sorry!

     


  5. 22 hours ago, Molly Mae said:

     

    Spoiler

    I considered this, but since Dick said another was lying, all of them can't be telling the truth.  I take "is lying" to mean "is lying today" and not "is lying right at this moment."  I also considered plays on the word "lying" (as in, lying down), but the correct form would be "laying" and absolute truth-tellers also don't make mistakes.

    The correct grammatical use for placing yourself in a horizontal position is "lying down", not "laying down", which has to have a direct object, i.e. laying something down). Lie down does not require a direct object. "Lieing" is not to tell the truth! Careful with the spelling!

    ;)

     


  6.  

    Thalia, I'll check your current numbering later, but ...

    Spoiler

    ... a big apology!

    Your first score was actually 7/16! Now you've changed 2 of the correct ones to incorrect and 2 other incorrect ones to correct.

    Thus, as your latest stab count stands, you again have 7/16.

    Sorry for my initial miss checking!

     

     


  7. One more try then!

    Spoiler

    Bert's statement referring to "make an equilateral triangle" (i.e the first Morley triangle) is only partially true. If all of the trisectors are intersected, one can obtain more than one equilateral triangle. Dick may then be telling the truth and refer to Bert as the lying brother. Probably not the answer yet!

     


  8. Another go ...

    On 1/4/2018 at 10:50 AM, bonanova said:
    • Spoiler

      Al: I was analyzing random groups of 3 numbers, and I found that if the numbers sum to zero then their product is the average of their cubes. (True)

      Bert: I was analyzing random polygons with 3 sides, and I found that if I trisected all their angles I could make an equilateral triangle. (True - Morley's trisector theorem)

      Chuck: I planted a dozen apple trees out in the orchard, and I found a way to make eighteen rows of 3 trees, each row being dead-on straight. (True - can be illustrated)

      Dick: I went out and ran 3 miles in the woods, and I figured out that one of my 3 (living) brothers is lying. (False?)

       

      How could DIck (whilst running in the woods) figure out beforehand what the later statements of the other three brothers (and his own) would be, i.e. "I did not kill Eddie"?

       

       

       

     


  9. Thank you Bonanova for your input!

    To all participants ...

    The 3-cubelet removal question has now been submitted as a separate new entry called "Cubicle Stack #2" since the thread sort of "got lost" in the original  Cubicle Stack discussion after having been solved!

    Spoiler

    Indeed, the images of the 22 solutions posted for the 2-cubelet removal ought to be very handy! But there are a whole lot of more combinations now. Happy playing around, if you have the time of course!

     


  10. Suppose 27 identical cubes are glued together to form a cubical stack, as illustrated below.

    image.png.1d35379223509669e07e1659355d1797.png

    If one of the small cubes is omitted, four distinct shapes are possible. If two of the small cubes are omitted rather than just one, twenty-two distinct shapes are possible (see previously submitted Cubicle Stack at BrainDen.com).

    Now, if three of the cubelets are omitted, how many distinct shapes are possible?

     


  11.  

     

    Spoiler

    Not the most elegant sketch, but here's one way to plant 12 trees in 18 rows of 3 each.

    image.png.f45712b989b60171b1bb02d9cf0cb362.png

    Thus, if Al and Chuck told the truth and Bert tried (but failed) to make a sketch for the inspector (none of the trisectors colinear), then Dick is the third truth teller. So far all four (living) brothers already got the blame, but it now appears that Bert is in trouble! Bert also mentioned that he "was analyzing random polygons with 3 sides" ... why didn't he say triangles?

     

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