HP Forum Archive 19

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Bowling Challenge Variation Message #1 Posted by Bill (Smithville, NJ) on 12 Aug 2010, 9:30 a.m. Don's bowling challenge has led me to come up with a variation on it. 1. Each throw of the ball results in a prime number of pins falling. 2. No gutter balls allowed. 3. The running frame totals are prime. What is highest game total? Confession - I do have one solution but I have don't know what the maximum total could be. Bill

Re: Bowling Challenge Variation Message #2 Posted by Don Shepherd on 12 Aug 2010, 4:07 p.m., in response to message #1 by Bill (Smithville, NJ) Well, let me start the "ball rolling" (sorry for the tired pun). Spares are tricky, I tried a couple of them and couldn't make much progress, but how about this for a start: frame 1 2 3 4 5 6 7 8 9 10 roll 2,5 3,3 2,2 3,3 5,3 3,3 3,3 2,2 3,3 5,3 cum. score 7 13 17 23 31 37 43 47 53 61

Re: Bowling Challenge Variation Message #3 Posted by Bill (Smithville, NJ) on 13 Aug 2010, 6:56 a.m., in response to message #2 by Don Shepherd Don, Very good. Spares are possible. Just to tease you, I have one solution with three spares in it. Bill

Re: Bowling Challenge Variation Message #4 Posted by Palmer O. Hanson, Jr. on 13 Aug 2010, 11:31 p.m., in response to message #1 by Bill (Smithville, NJ) frame 1 2 3 4 5 6 7 8 9 10 roll 5,5 3,1 3,3 7,1 5,5 2,2 3,3 3,3 1,7 5,5 2 cum. score 13 17 23 31 43 47 53 59 67 79

Re: Bowling Challenge Variation Message #5 Posted by Don Shepherd on 13 Aug 2010, 11:37 p.m., in response to message #4 by Palmer O. Hanson, Jr. Palmer, at the risk of starting world war III, 1 is not a prime number. Don

Re: Bowling Challenge Variation Message #6 Posted by Katie Wasserman on 14 Aug 2010, 2:06 a.m., in response to message #5 by Don Shepherd 1 is not a prime but the modern definition, but it used to be considered so and not all that long ago. Besides, this would be an excellent reason for WW III, it sure beats race, land, resources and religion. Edited: 14 Aug 2010, 2:08 a.m.

Re: Bowling Challenge Variation Message #7 Posted by Bill (Smithville, NJ) on 14 Aug 2010, 2:34 p.m., in response to message #4 by Palmer O. Hanson, Jr. Hi Palmer, Well, I hadn't really considered 1 as a prime, but as Katie showed, it could be. Good solution using 1's, and three spares. As far as I can tell, 79 is the maximum that can be achieved without considering one as a prime. So it's interesting that by using 1, 79 can still be achieved. I tried starting with 83 & 89 and working the frames backwards from the tenth frame with no success. Bill

My non-geezer solutions Message #8 Posted by Palmer O. Hanson, Jr. on 14 Aug 2010, 9:29 p.m., in response to message #1 by Bill (Smithville, NJ) Since one isn't considered to be a prime number in modern times I will have to admit that a solution using ones is a geezer solution. The solutions below which don't use ones are my non-geezer solutions: frame 1 2 3 4 5 6 7 8 9 10 roll 5,5 3,3 2,2 5,3 5,5 2,2 3,3 3,5 3,3 5,5 2 cum. score 13 19 23 31 43 47 53 61 67 79 and a second solution only changes the first two frames frame 1 2 3 4 5 6 7 8 9 10 roll 5,2 5,5 2,2 5,3 5,5 2,2 3,3 3,5 3,3 5,5 2 cum. score 7 19 23 31 43 47 53 61 67 79 where both solutions yield 79, and I agree with Bill that a score of 79 may be the maximum attainable. Palmer

Re: My non-geezer solutions Message #9 Posted by Bill (Smithville, NJ) on 15 Aug 2010, 6:37 a.m., in response to message #8 by Palmer O. Hanson, Jr. Hi Palmer, Your second one matches the one I came up with. I had tried several times to get a spare to work in the first frame, with no success. But I now see it is possible. Thanks, Bill

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