Announcement

Collapse
No announcement yet.

Puzzles with numbers and things

Collapse
X
Collapse
 
  • Page of 238
  • Filter
  • Time
  • Show
Clear All
new posts
Previous 1 4 44 51 52 53 54 55 56 57 64 104 154 238 template Next
  • #796
    Originally Posted by abextra
    Poor little Oliver... Does he have any chance at all? It seems to me, here goes another point to davis_greatest.
    Yes, he does have a chance It's just none of the chances that have been suggested so far


    snookersfun, I'll do your question in a minute and PM you the answer...
    "If anybody can knock these three balls in, this man can."
    David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

    Comment

    • #797
      A clue to round 59!

      Originally Posted by davis_greatest
      Charlie and Oliver are playing Big Ape Break, and are level on points... it has gone to a respotted black - they have each had a few shots, but no one has potted it yet.

      Charlie always has the same chance of potting the black with every shot he plays, no matter what the position of the balls - and the same goes for Oliver; but, at each attempt, Charlie is twice as likely to pot it as Oliver is.

      Also, with each attempt, Charlie is as likely to pot the black as Oliver is to miss it and, of course, Oliver is as likely to pot the black as Charlie is to miss it. Neither ape will ever foul.

      Charlie is about to take the next shot. What are Oliver's chances of winning the frame?


      OK, I'll give a clue, as this question seems to have resisted all attempts / guesses so far!

      One way to look at it is to note that:

      1) Oliver can win in two ways: by potting the black at his first shot, or by potting the black any time after his first shot. Those can't both occur. So his chance of winning is the sum of those two chances.

      2) If Charlie and Oliver both miss with their first shots, then it will be Charlie's shot again and we will be back where we started - so Oliver's chance from that point will be the same as it was at the beginning.
      "If anybody can knock these three balls in, this man can."
      David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

      Comment

      • #798
        1/3 + 1/9?????

        Comment

        • #799
          Originally Posted by snookersfun
          1/3 + 1/9?????
          No, not 4/9, but I think we've had almost every fraction in existence except the correct one!
          "If anybody can knock these three balls in, this man can."
          David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

          Comment

          • #800
            we know, that it is bigger than 1/9 and shouldn't we assume that it is smaller than 1/3 really, as Oliver has a 2/3 chance of sinking the ball at his go?
            1/4+1/9?

            Comment

            • #801
              I propose, you give yourself this point and explain already. I am really curious.

              Comment

              • #802
                Originally Posted by snookersfun
                we know, that it is bigger than 1/9 and shouldn't we assume that it is smaller than 1/3 really, as Oliver has a 2/3 chance of sinking the ball at his go?
                Yes, bigger than 1/9. Yes, smaller than 1/3.

                Originally Posted by snookersfun
                1/4+1/9?
                No, that would be 13/16... it is simpler than that!
                "If anybody can knock these three balls in, this man can."
                David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

                Comment

                • #803
                  Originally Posted by snookersfun
                  I propose, you give yourself this point and explain already. I am really curious.
                  I'll give it a little while longer! Someone is bound to solve it.... ?
                  "If anybody can knock these three balls in, this man can."
                  David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

                  Comment

                  • #804
                    Could you tell me where I went wrong in my solution? I honestly can't find where my error is!
                    "I'll be back next year." --Jimmy White

                    Comment

                    • #805
                      Originally Posted by elvaago
                      Could you tell me where I went wrong in my solution? I honestly can't find where my error is!
                      The one below?

                      Originally Posted by elvaago
                      Let me type out my solution, can you tell me where I went wrong?
                      Let's say Charlie potting is CP, charlie missing is CM, Oliver potting is OP and Oliver missing is OM.

                      CP = 2 OP
                      CP = OM
                      CM = OP

                      OM + OP = 1
                      2OM + 2OP = 2
                      2OM + CP = 2
                      2CP + CP = 2
                      3CP = 2
                      CP = 2/3
                      CM = OP = CP/2 = 1/3
                      Yes, with each attempt, Charlie has a 2/3 chance of success, and Oliver a 1/3 chance. Right so far - then comes the real part of the question.

                      Originally Posted by elvaago
                      OK I see where I went wrong originally.
                      For Oliver to win, Charlie needs to miss and then Oliver needs to pot. 1/3 * 1/3 = 1/9. That's my final answer and if it's wrong, someone else can get it. ;-)
                      What you are showing here is the chance that Oliver wins on his first shot. But if he doesn't and he misses, he's not out of the game yet - he might get back to the table! You haven't allowed for that....
                      "If anybody can knock these three balls in, this man can."
                      David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

                      Comment

                      • #806
                        5/27????? I won't claim points, promise

                        Comment

                        • #807
                          Oliver winning at first attempt: 1/9
                          Oliver winning at second attempt: 1/3*2/3*1/9
                          Oliver winning at third attempt: 1/3*2/3*1/3*2/3*1/9

                          Oliver winning at nth attempt: (n-1)(1/3 * 2/3) * 1/9

                          How's that!
                          "I'll be back next year." --Jimmy White

                          Comment

                          • #808
                            Originally Posted by snookersfun
                            5/27????? I won't claim points, promise
                            No! But you're close... in that it is a fraction.
                            "If anybody can knock these three balls in, this man can."
                            David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

                            Comment

                            • #809
                              Originally Posted by elvaago
                              Oliver winning at first attempt: 1/9
                              Oliver winning at second attempt: 1/3*2/3*1/9
                              Oliver winning at third attempt: 1/3*2/3*1/3*2/3*1/9

                              Oliver winning at nth attempt: (n-1)(1/3 * 2/3) * 1/9

                              How's that!
                              Good - getting there.... closest attempt yet, but unfortunately the line for winning at nth attempt is wrong.

                              And I don't want the chance that he wins at the "nth attempt" - I want the chance that he wins the game (whenever it might be)!
                              "If anybody can knock these three balls in, this man can."
                              David Taylor, 11 January 1982, as Steve Davis prepared to pot the blue, in making the first 147 break on television.

                              Comment

                              • #810
                                Originally Posted by davis_greatest
                                No! But you're close... in that it is a fraction.
                                Ha! Take another one then 11/81

                                Comment

                                Previous 1 4 44 51 52 53 54 55 56 57 64 104 154 238 template Next
                                Working...
                                X