Bowling Challenge Variation

[Bill (Smithville, NJ)]

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

[Don Shepherd]

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

[Bill (Smithville, NJ)]

Don,

Very good. Spares are possible. Just to tease you, I have one solution with three spares in it.

Bill

[Palmer O. Hanson, Jr.]

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

[Don Shepherd]

Palmer, at the risk of starting world war III, 1 is not a prime number.

Don

[Katie Wasserman]

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.

[Bill (Smithville, NJ)]

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

[Palmer O. Hanson, Jr.]

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

[Bill (Smithville, NJ)]

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