All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Games
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Just part 1. (beats my answer for part 1) | Comment 3 of 10 |
(In reply to Just part 1. by Leming)

Private Sub cmdStart_Click()

 goingBack = ""
 Play 1
 Print sCtr
 Print "ended"

 End Sub
 

Sub ReportIt()
If Frame(10) < maxScore Then Exit Sub
maxScore = Frame(10)
  Cls
  sCtr = sCtr + 1
  For I = 1 To throwNo
   If I > throwNo Then Exit For
   If Throw(I) = 10 Then Print " x    "; Else Print Throw(I);: I = I + 1: Print Throw(I);
  Next
   Print
  For I = 1 To 10
   Print Frame(I);: Print " ";
  Next
   Print: Print sCtr
End Sub

Sub Play(Fr)
  DoEvents
  spareFlag = 0
  If Fr = 3 Or Fr = 6 Or Fr = 9 Then setVal = 10 Else setVal = 1
  For N = 10 To setVal Step -1
   throwNo = throwNo + 1
   Throw(throwNo) = N
   If N < 10 Then
     For N2 = 0 To 10 - N
      throwNo = throwNo + 1
      Throw(throwNo) = N2
      If goingBack = "xx" Then
        Frame(Fr - 2) = Frame(Fr - 2) + N
        Frame(Fr - 1) = Frame(Fr - 1) + N + N2
        Frame(Fr) = Frame(Fr - 1) + N + N2
        If N2 = 10 - N Then goingBack = "/" Else goingBack = ""
        If fnIsPrime(Frame(Fr - 2)) And fnIsPrime(Frame(Fr - 1)) Then
          If goingBack = "/" Or fnIsPrime(Frame(Fr)) Then
            If Fr = 10 Then
             If goingBack = "/" Then
              For N3 = 0 To 10 - N1 - N2
               throwNo = throwNo + 1
               Throw(throwNo) = N3
               Frame(Fr) = Frame(Fr) + N3
               If fnIsPrime(Frame(Fr)) Then ReportIt
               Frame(Fr) = Frame(Fr) - N3
               throwNo = throwNo - 1
              Next
             Else
              ReportIt
             End If
            Else
              Play Fr + 1
            End If
          End If
         End If
        Frame(Fr - 2) = Frame(Fr - 2) - N
        Frame(Fr - 1) = Frame(Fr - 1) - N - N2
        Frame(Fr) = 0
        goingBack = "xx"
      ElseIf goingBack = "x" Then
        If N2 < 10 - N Or spareFlag = 0 Then
            Frame(Fr - 1) = Frame(Fr - 1) + N + N2
            Frame(Fr) = Frame(Fr - 1) + N + N2
            If N2 = 10 - N Then goingBack = "/": spareFlag = 1 Else goingBack = ""
            If fnIsPrime(Frame(Fr - 1)) Then
              If goingBack = "/" Or fnIsPrime(Frame(Fr)) Then
                If Fr = 10 Then
                 If goingBack = "/" Then
                  For N3 = 0 To 10 - N1 - N2
                   throwNo = throwNo + 1
                   Throw(throwNo) = N3
                   Frame(Fr) = Frame(Fr) + N3
                   If fnIsPrime(Frame(Fr)) Then ReportIt
                   Frame(Fr) = Frame(Fr) - N3
                   throwNo = throwNo - 1
                  Next
                 Else
                  ReportIt
                 End If
                Else
                  Play Fr + 1
                End If
              End If
             End If
            Frame(Fr - 1) = Frame(Fr - 1) - N - N2
            Frame(Fr) = 0
            goingBack = "x"
        End If
      ElseIf goingBack = "/" Then
        Frame(Fr - 1) = Frame(Fr - 1) + N
        Frame(Fr) = Frame(Fr - 1) + N + N2
        If N2 = 10 - N Then goingBack = "/" Else goingBack = ""
        If fnIsPrime(Frame(Fr - 1)) Then
          If goingBack = "/" Or fnIsPrime(Frame(Fr)) Then
            If Fr = 10 Then
             If goingBack = "/" Then
              For N3 = 0 To 10 - N1 - N2
               throwNo = throwNo + 1
               Throw(throwNo) = N3
               Frame(Fr) = Frame(Fr) + N3
               If fnIsPrime(Frame(Fr)) Then ReportIt
               Frame(Fr) = Frame(Fr) - N3
               throwNo = throwNo - 1
              Next
             Else
              ReportIt
             End If
            Else
              Play Fr + 1
            End If
          End If
         End If
        Frame(Fr - 1) = Frame(Fr - 1) - N
        Frame(Fr) = 0
        goingBack = "/"
      Else
        If N2 < 10 - N Or spareFlag = 0 Then
            Frame(Fr) = Frame(Fr - 1) + N + N2
           
            If N2 = 10 - N Then goingBack = "/": spareFlag = 1 Else goingBack = ""
              If goingBack = "/" Or fnIsPrime(Frame(Fr)) Then
                If Fr = 10 Then
                 If goingBack = "/" Then
                  For N3 = 0 To 10 - N1 - N2
                   throwNo = throwNo + 1
                   Throw(throwNo) = N3
                   Frame(Fr) = Frame(Fr) + N3
                   If fnIsPrime(Frame(Fr)) Then ReportIt
                   Frame(Fr) = Frame(Fr) - N3
                   throwNo = throwNo - 1
                  Next
                 Else
                  ReportIt
                 End If
                Else
                  Play Fr + 1
                End If
              End If
            Frame(Fr) = 0
            goingBack = ""
        End If
      End If
      throwNo = throwNo - 1
     Next
   Else
     ' have a strike
     If goingBack = "xx" Then
       Frame(Fr - 2) = Frame(Fr - 2) + 10
       Frame(Fr - 1) = Frame(Fr - 1) + 10
       Frame(Fr) = Frame(Fr - 1) + 10
       If Fr = 10 Then
        If fnIsPrime(Frame(Fr - 2)) Then
         For N2 = 0 To 10
          For N3 = 0 To 10
           Frame(Fr - 1) = Frame(Fr - 1) + N2
           Frame(Fr) = Frame(Fr - 1) + 10 + N2 + N3
            Throw(throwNo + 1) = N2: Throw(throwNo + 2) = N3
            throwNo = throwNo + 2
              If fnIsPrime(Frame(Fr - 1)) And fnIsPrime(Frame(Fr)) Then
               ReportIt
              End If
            throwNo = throwNo - 2
           Frame(Fr - 1) = Frame(Fr - 1) - N2
           Frame(Fr) = 0
          Next
         Next
        End If
       Else
         Play Fr + 1
       End If
       Frame(Fr - 2) = Frame(Fr - 2) - 10
       Frame(Fr - 1) = Frame(Fr - 1) - 10
       Frame(Fr) = 0
     ElseIf goingBack = "x" Then
       Frame(Fr - 1) = Frame(Fr - 1) + 10
       Frame(Fr) = Frame(Fr - 1) + 10
       If Fr = 10 Then
         For N2 = 0 To 10
          For N3 = 0 To 10
           Frame(Fr - 1) = Frame(Fr - 1) + N2
           Frame(Fr) = Frame(Fr - 1) + 10 + N2 + N3
            Throw(throwNo + 1) = N2: Throw(throwNo + 2) = N3
            throwNo = throwNo + 2
              If fnIsPrime(Frame(Fr - 1)) And fnIsPrime(Frame(Fr)) Then
               ReportIt
              End If
            throwNo = throwNo - 2
           Frame(Fr - 1) = Frame(Fr - 1) - N2
           Frame(Fr) = 0
          Next
         Next
       Else
        goingBack = "xx"
         Play Fr + 1
        goingBack = "x"
       End If
       Frame(Fr - 1) = Frame(Fr - 1) - 10
       Frame(Fr) = 0
     ElseIf goingBack = "/" Then
       Frame(Fr - 1) = Frame(Fr - 1) + 10
       Frame(Fr) = Frame(Fr - 1) + 10
       If Fr = 10 Then
         For N2 = 0 To 10
          For N3 = 0 To 10
           Frame(Fr) = Frame(Fr - 1) + 10 + N2 + N3
            Throw(throwNo + 1) = N2: Throw(throwNo + 2) = N3
            throwNo = throwNo + 2
              If fnIsPrime(Frame(Fr - 1)) And fnIsPrime(Frame(Fr)) Then
               ReportIt
              End If
            throwNo = throwNo - 2
           Frame(Fr) = 0
          Next
         Next
       Else
        goingBack = "x"
         Play Fr + 1
        goingBack = "/"
       End If
       Frame(Fr - 1) = Frame(Fr - 1) - 10
       Frame(Fr) = 0
     Else
       Frame(Fr) = Frame(Fr - 1) + 10
       If Fr = 10 Then
         For N2 = 0 To 10
          For N3 = 0 To 10
           Frame(Fr) = Frame(Fr - 1) + 10 + N2 + N3
            Throw(throwNo + 1) = N2: Throw(throwNo + 2) = N3
            throwNo = throwNo + 2
              If fnIsPrime(Frame(Fr)) Then
               ReportIt
              End If
            throwNo = throwNo - 2
           Frame(Fr) = 0
          Next
         Next
       Else
        goingBack = "x"
         Play Fr + 1
        goingBack = ""
       End If
       Frame(Fr) = 0
     End If
   End If
   throwNo = throwNo - 1
  Next

End Sub


 Function fnIsPrime(Num)
   Select Case Num
   Case 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, _
257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401
     r = 1
   Case Else
     r = 0
  End Select
  fnIsPrime = r

 End Function

Many ways were found of getting a score of 211, the maximum that my program found in the time I allotted it.

Part 1. 211:

9 1  3 7  8 2  x    9 1  x    x    2 8  x    x   x x
 13   31   51   71   91  113  131  151  181  211


 
Of course the lowest possible score would be the trivial 2, completed in the first frame and repeated all the way down:

alternate to part 1 -- trying for lowest score:

2 0  0 0  0 0  0 0  0 0  0 0  0 0  0 0  0 0  0 0
  2    2    2    2    2    2    2    2    2    2

  Posted by Charlie on 2007-11-28 15:47:58
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information