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rocdocmac

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Posts posted by rocdocmac

  1. Spoiler

    Al must have opened a box containing either BBB or WWB. Since the label was wrong, the true content was either WWB

    or BBB. Therefore, he knew the color of his third ball.

    Bert opened a box with either WBB or WWB, leaving him the choice of either WWB or WBB (according to the label) and

    he could guess the color of his third ball.

    Cal's box could have had either WWW or WWB and could thus  not know the color of the third ball.

    So, the labels that stated "WBB", "WWB" and "BBB" could only be interpreted as having the combinations BBB, WBB

    and another (yet unknown) combination.

    Don followed the conversations and then knew for sure that his box contained the combination WWB (Cal could not

    have had that combination - only WWW was possible for Cal).

     

    Al: BBB

    Bert: WBB

    Cal: WWW

    Don: WWB

     

     

  2. I've changed the amounts won by the winners to make it a bit easier (in a way). The original one proved to be too tough!

    Humble apologies to those who have spent their valuable time by working on the previous OP.

    The revised OP now reads as follows:

     

    In a recent Lotto draw, Jeremiah won $790, Philemon $1650, and Ridgeley $464.

    How much did Waltraud and Xhuliana win in the same draw?

  3. Suppose there is an international football (soccer) team consisting of 20 players and selected as follows from five countries:
     
    Two players from Spain
    Three from Italy
    Four from France
    Five from Brazil
    Six from Germany
     
    The squad only includes one goalkeeper, who plays for an Italian club, whereas the captain plays for a French club.
    Assuming the goalkeeper and the captain are included in every selection of eleven players, how many different teams
    could be selected from the twenty players (irrespective of position) if at least three German club players are
    included in each selection?
  4. In a recent Lotto draw, Jeremiah won $1138, Philemon $634, and Ridgeley $205.

    How much did Waltraud and Xhuliana win in that draw?

    Edit: Jeremiah won $790, Philemon $1650, and Ridgeley $464

  5. On 5/15/2019 at 4:24 PM, plasmid said:

    The only thing I'd say, though, is that if you drop a breadcrumb in region E, it seems like the mouse would go eat the breadcrumb there and then go to either B or D instead of C -- either of those two points would be closer to region E than C is.

    So I see!

    Spoiler

    So, mouse moves from A → F → C → B/D → D/B

    blob.png.2da017ce8847276305a2a800abe94c8d.png

     

     

  6. Just to get my own mind at peace (square case) ...

    Spoiler

    One extra crumb in one of the orange regions (E or F) between center O and X or between O and Y, but not at X, Y or O,

    since BC=CD=CX=AY and BO=CO=DO (equidistances).

    Mouse moves from A to E (or F) to C, then to B (or D), and finally to D (or B).

     

    blob.png.d1e422dc9fa813b7152b1f781383579f.png

     

  7. My revised answers sent in previously were not all correct. These should be fine ...

    Spoiler

    With impossible triangles/straight-line cases:

    Equilateral (EL) = 2/72 (1/36)

    Acute isosceles (AI) =  15/72 (5/24)

    Obtuse isosceles (OI) =  6/72 (1/12)

    Impossible triangles (including "straight line" cases) = 9/72 (1/8) 

    Normal non-isosceles triangles = 40/72 (5/9)

    Total isosceles (AI+OI) = 21/72 (7/24)

    Including equilateral (AI+OI+EL) = 23/72

     

    Without impossible triangles/straight-line cases:

    Equilateral (EL) = 2/63

    Acute isosceles (AI) =  15/63 (5/21)

    Obtuse isosceles (OI) =  6/63 (2/21)

    Normal non-isosceles triangles = 40/63

    Total isosceles (AI+OI) = 21/63 (1/3)

    Including equilateral (AI+OI+EL) = 23/63

  8. Revised ...

    Spoiler

    I was way out with my first attempt!

    Equilateral (EL) = 2/72 = (1/36)

    Acute isosceles (AI) =  16/72 (2/9)

    Obtuse isosceles (OI) =  5/72

    Impossible triangles = 9/72 (1/8) 

    Normal triangles = 40/72 (5/9)

    Total isosceles (AI+OI) = 18/72 (1/4)

    Including equilateral (AI+OI+EL) = 23/72

     

     

  9. In a nutshell ...

    Spoiler

    There are 216 possible outcomes with three dice forming ...

    Equilateral triangles: 6/216 (1/36)

    No isosceles triangles: 120/216 (5/9)

    Acute isosceles triangles: 45/216 (5/24)

    Obtuse isosceles triangles: 45/216 (5/24)

    All isosceles triangles (including equilateral triangles): 96/216 (4/9)

     

  10. I thought that, if anyone who still wants to know the answer, it follows below ...

    Clues by those who knew the answer (or have learned it) were starting to show up all over the place (remorse, S & O, transmitted, Message In A Bottle lyrics at end of verse (SOS repeated) and title of ABBA song (SOS).

    For people that are still battling with their brain, the characters come from the International Morse Code in ascending order of "dots" or "dashes"

    Thus ...

    image.png.365c0595d59d4906da52f0e9f985a886.png

     "SOS" =image.png.9146632fca5e48f58c407e52eac3a1f7.png   

    Originally, SOS did not actually stand for anything (e.g. "Save Our Souls"). It was used since the letters S and O are easy to make and are distinctive.

     

     

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