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Final Scores at the PrimeBowl (Posted on 2007-11-28) Difficulty: 3 of 5
1. What is the highest score you can obtain in a standard game of bowling if your cumulative score in each of the ten frames is required to be a prime number?

2. What is the lowest score you can obtain in a standard game of bowling if your cumulative score in each of the ten frames is required to be a prime number and for each throw you knock down a prime number of pins?

The next two questions refer to 3-6-9 bowling. The difference in 3-6-9 bowling and the standard game is the 3rd, 6th and 9th frame already have strikes recorded.

3. What is the highest score you can obtain in a game of 3-6-9 bowling if your cumulative score in each of the ten frames is required to be a prime number?

4. What is the lowest score you can obtain if your cumulative score in each of the ten frames is required to be a prime number and for each throw (excluding the pre-recorded throws) you knock down a prime number of pins?

The first score sheet represents Games #1 and #2.
The second is for use with Games #3 and #4.

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

X

X

X

One Scoring reference is here should you need one.

See The Solution Submitted by Dej Mar    
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re(2): and just part 3 (and part 4). -- same scores, different ways, other alternates | Comment 7 of 10 |
(In reply to re: and just part 3 (and part 4). -- same scores, different ways, other alternates by Charlie)

Charlie,
I highly respect your mathematical skill, programming and analysis (and many other attributes you've presented here on perplexus) -- but, here, I've found some problems.

 

As in your solution to Part 3 for strike-strike-spare, the first strike is calculated correctly, but the second strike seems to miss adding both throws following the strike.

x  x  2-8 x

53 71 91  ... 

should instead calculate to be  

53 73 93  ... but, of course, 93 isn’t prime.

 

Another problem I found is in your solution for Part 2, you’ve somehow included zero as being a prime number.


  Posted by Dej Mar on 2007-11-28 20:11:39
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