Let's play Mölkky!

Question

Mölkky

Mölkky is a Finnish throwing game. The players use a wooden pin (also called "mölkky") to try to knock over wooden pins of almost similar dimensions with the throwing pin, marked with numbers from 1 to 12. The initial position of the pins is as follows:

   (07)(09)(08)
 (05)(11)(12)(06)
   (03)(10)(04)
     (01)(02)

^{This description and the rules below are based on Wikipedia.}

Simplified Mölkky rules

1. Knocking over one pin scores the number of points marked on the pin.

2. Knocking 2 or more pins scores the number of pins knocked over (e.g., knocking over 3 pins scores 3 points).

3. The aim of the game is to reach exactly 50 points. Scoring more than 50 is penalized by setting the score back to 25 points.

4. For the purpose of this challenge, we will make the assumption that the pins are always in the exact order described above. (In a real game, the pins are stood up again after each throw in the location where they landed.)

All other Mölkky rules are ignored and only a single player is considered.

Input

A non-empty list of lists of 12 booleans. Each list of booleans describes the outcome of a throw: 1 if the pin was knocked over and 0 otherwise. The booleans are given in the exact order of the pins, from top left to bottom right: 7, 9, 8, 5, 11, 12, 6, 3, 10, 4, 1, 2.

Output

The score after all throws described in the input, calculated by applying rules 1, 2 and 3.

Detailed example

Let's consider the following input:

// 07 09 08 05 11 12 06 03 10 04 01 02
[ [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],  // scores 5 (rule #1)
  [ 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],  // scores 2 (rule #2), total: 7
  [ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1 ],  // scores 7, total: 14
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],  // scores 12, total: 26
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],  // scores 12, total: 38
  [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],  // scores 11, total: 49
  [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],  // scores 7, total: 56 -> 25 (rule #3)
  [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] // scores 2, total: 27

The expected output is 27.

Challenge rules

• You may take input in any reasonable format. Instead of lists of booleans, you can use integers where the most significant bit is the pin #7 and the least significant bit is the pin #2. In this format, the above example would be passed as [ 256, 2304, 127, 64, 64, 128, 2048, 3072 ].
• The input list may contain throws where no pin at all is knocked over, in which case the score is let unchanged.
• You don't have anything special to do when the score reaches exactly 50 points. But you can assume that no other throw will follow when it happens.
• This is code-golf, so the shortest answer in bytes wins.

Test cases

Using lists of integers as input:

[ 0 ] --> 0
[ 528 ] --> 2
[ 4095 ] --> 12
[ 64, 0, 3208 ] --> 16
[ 16, 1907, 2048 ] --> 18
[ 2023, 2010, 1, 8 ] --> 29
[ 1726, 128, 35, 3136, 1024 ] --> 34
[ 32, 32, 2924, 2, 256, 16 ] --> 28
[ 64, 64, 2434, 1904, 3251, 32, 256 ] --> 25
[ 3659, 2777, 2211, 3957, 64, 2208, 492, 2815 ] --> 25
[ 2047, 1402, 2, 2599, 4, 1024, 2048, 3266 ] --> 50
[ 256, 2304, 127, 64, 64, 128, 2048, 3072 ] --> 27
[ 16, 8, 128, 1, 2048, 1, 2048, 513, 8, 3206 ] --> 30

You can follow this link to get these test cases in Boolean format.

Answer 1

Python 2, 126 111 108 104 bytes

-3 bytes thanks to Jonathan Allan

-4 bytes thanks to Kaya!

f=lambda A,t=0:t>50and f(A,25)or A and f(A[1:],t-~(sum(A[0])-1or 762447093078/12**A[0].index(1)%12))or t

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Defines a recursive function that takes a 2D array of 1s and 0s and returns an integer value. Nothing too special in the construction, and I'm sure there's a simpler solution.

Explanation:

f=lambda A,t=0:    #Define the function, initialising t to 0 on the first iteration
               t>50and f(A,25)      #If t>50 then iterate again with t=25
                              or    #Else
               A and                #If A exists
                     f(A[1:],       #Iterate again without the first list of A
                        t-~         #And add to t, either
                           (sum(A[0])-1   #The sum of all elements if that's not 1
                                         or
                           762447093078/12**A[0].index(1)%12   #Else the appropriate pin value (black magic!)
               or t       #Finally, if A is finished, just return t

Answer 2

Jelly, 25 bytes

“ñ€bḷ’œ?TLḢṖ?µ€+25¹>?50ɗ/

A monadic link accepting a list of lists of ones and zeros (each of length 12) which returns an integer.

Try it online! Or see the test-suite (using the integer values given in the OP)

How?

This solution makes use of, œ?, which given a number, n, and a list finds the n^th lexicographical permutation of the list where the list defines the sort order. First we need to work out this n:

 index:  1  2  3  4  5  6  7  8  9 10 11 12
 value:  7  9  8  5 11 12  6  3 10  4  1  2   (as defined by the question)
     P: 11 12  8 10  4  7  1  3  2  9  5  6   (our permutation lookup array)

...that is, P at index i is set to the original index of the value i.
This P has a lexicographical index of 438,337,469 (that is, if you took all 12! permutations of the numbers 1 to 12 and sorted them lexicographically, the 438,337,469^th would be P).
This may be found using Jelly's Œ¿ atom.
Both steps may be performed in one go using the Jelly program ĠŒ¿

“ñ€bḷ’œ?TLḢṖ?µ€+25¹>?50ɗ/ - Link: list of lists of zeros and ones
             µ€           - perform the monadic chain to the left for €ach list:
“ñ€bḷ’                    -   base 250 number = 438337469
      œ?                  -   nth permutation (reorder the 1s and 0s to their pin values)
        T                 -   truthy indices (get the pin values of the 1s)
            ?             -   if...
           Ṗ              -   ...condition: pop (length greater than 1 ?)
         L                -   ...then: length (the number of pins)
          Ḣ               -   ...else: head (the first (& only) pin value)
                        / - reduce the resulting list of integers with:
                       ɗ  -   last three links as a dyad:
               +          -     addition (add the two values together)
                     50   -     literal fifty
                    ?     -     if...
                   >      -     ...condition: greater than (sum greater than 50 ?)
                25        -     ...then: literal twenty-five
                  ¹       -     ...else: identity (do nothing - just yield the sum)

Answer 3

Python 2, 90 bytes

^{Heavily inspired by Jo King's Python 2 answer and utilising Kaya's base-12 representation comment}

t=0
for v in input():t+=sum(v)-1or 762447093078/12**v.index(1)%12;t=[t+1,25][t>49]
print t

Try it online! Or see the test-suite

Answer 4

Pyth, 51 48 38 bytes

VQI>=+Z?qJsN1@.PC"îO&"S12xN1J50=Z25;Z

Saved 10 bytes thanks to Jonathan Allan Takes input as a list of lists of booleans.
Try it here

Explanation

VQI>=+Z?qJsN1@.PC"îO&"S12xN1J50=Z25;Z
VQ                                  ;     For each input...
    =+Z                                   ... add to the total...
       ?q sN1                             ... if one pin is down...
             @.PC"îO&"S12xN1              ... the score of that pin.
         J                    J           ... otherwise, the count.
  I>                           50         If we pass 50...
                                 =Z25     ... reset to 25.
                                     Z    Output the total.

Answer 5

Perl 5, 74 70 bytes

$\+=y/1//-1||/1/g&&(0,6,8,7,4,10,11,5,2,9,3,0,1)[pos];$\=25if++$\>50}{

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Takes input as a series of newline separated bitstrings.

Answer 6

05AB1E, 29 28 bytes

v•CÞŸαLć•13вyOΘmyÏOO25‚¬50›è

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Explanation

v                              # for each boolean list in input
 •CÞŸαLć•                      # push 13875514324986
         13в                   # convert to a list of base-13 numbers
            yO                 # push the sum of y
              Θm               # truthify and raise the pin-list to this number (0 or 1)
                yÏ             # keep those which are true in the current list
                  OO           # sum the list and the stack
                    25‚        # pair with 25
                       ¬50›    # check if the first number is larger than 50
                           è   # index into the pair with this result

Answer 7

Java 10, 131 130 129 bytes

m->{int r=0,i,s,t;for(var a:m){for(i=s=t=0;i<12;s+=a[i++])t=a[i]>0?"    \n".charAt(i):t;r+=s<2?t:s;r=r>50?25:r;}return r;}

Contains 10 unprintables.
Input as integer-matrix of zeros and ones.

-1 byte thanks to @JonathanFrech, changing \t into an actual tab (works in TIO, doesn't work in my local IDE).

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Explanation:

m->{                // Method with integer-matrix parameter and integer return-type
  int r=0,          //  Result-integer, starting at 0
      i,s,t;        //  Temp integers
  for(var a:m){     //  Loop over the integer-arrays of the input
    for(i=s=t=0;    //   Reset `i`, `s` and `t` to 0
        i<12;       //   Loop `i` in the range [0,12)
        s+=a[i++])  //    Increase `s` by the current value (0 or 1)
      t=a[i]>0?     //    If the current value is 1:
         "  \n".charAt(i)
                    //     Set `t` to the score at this position
        :t;         //    Else: Leave `t` the same
    r+=s<2?         //   If only a single pin was hit:
        t           //    Add its score `t` to the result
       :            //   Else:
        s;          //    Add the amount of pins `s` to the result
    r=r>50?         //   If the result is now above 50
       25           //    Penalize it back to 25
      :r;}          //   If not, it stays the same
  return r;}        //  Return the result

Answer 8

Haskell, 96 bytes

foldl(\s a->([s..50]++e)!!sum(last$zipWith(*)[7,9,8,5,11,12,6,3,10,4,1,2]a:[a|sum a>1]))0
e=25:e

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The wrapping is clever: I essentially index at position s+sum(…) into the list ([0..50]++cycle[25]). However, a shorter way to write that is indexing at position sum(…) and beginning the list at s.

Answer 9

Charcoal, 43 bytes

≔⁰ηＦθ«≧⁺⎇⊖ΣιΣι⌕᧔$｜#z⁸Ｕg⊗”⌕ι¹η¿›η⁵⁰≔²⁵η»Ｉη

Try it online! Link is to verbose version of code. Takes input as a boolean array. Explanation:

≔⁰η

Set the score to 0.

Ｆθ«

Loop over the throws.

⎇⊖Σι

Is the number of pins 1?

Σι

If not, then take the number of pins.

⌕᧔$｜#z⁸Ｕg⊗”⌕ι¹

Otherwise, translate the position of the pin to a value.

≧⁺...η

Add it to the score.

¿›η⁵⁰≔²⁵η

If the score exceeds 50 then set it back to 25.

»Ｉη

Print the final result after all the throws.

Answer 10

Husk, 47 35 bytes

_{-12 bytes thanks to H.PWiz (better way of generating the list encoding points)!}

F₅0
S?25>50+?←Lε`f`+Nm+3d4652893071

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Explanation

F₅0  -- input is a list of boolean lists
F    -- left fold by
 ₅   -- | the function flipped (overflowing label) on line 1
  0  -- | with initial value 0

S?25>50+?←Lε`f`+Nm+3d4652893071  -- example inputs: [0,0,0,1,0,0,0,0,0,0,0,0] 0
                     4652893071  -- integer literal: 4652893071
                    d            -- digits: [4,6,5,2,8,9,3,0,7,1]
                 m+3             -- map (+3): [7,9,8,5,11,12,6,3,10,4]
              `+N                -- append natural numbers: [7,9,8,5,11,12,6,3,10,4,1,2,3,...
            `f                   -- filter this list by argument: [5]
        ?  ε                     -- if it's of length 1
         ←                       -- | take first
          L                      -- | else the length
                                 -- : 5
       +                         -- add to argument: 5
 ?  >50                          -- if the value is > 50
  25                             -- | then 25
S                                -- | else the value
                                 -- : 5

Answer 11

Haskell, 110 bytes

m s|sum s==1=sum$zipWith(*)[7,9,8,5,11,12,6,3,10,4,1,2]s|1>0=sum s
f l=foldl(\b->c.(b+).m)0l
c a|a>50=25|1>0=a

Same length: f l=foldl(\b a->last$b+m a:[25|b+m a>50])0l instead of f and c

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Answer 12

Red, 189 172 bytes

func[b][s: 0 foreach c b[d: 0 foreach e c[if e = 1[d: d + 1]]i: find c 1
n: either i[pick[7 9 8 5 11 12 6 3 10 4 1 2]index? i][0]if 50 < s: s + either 1 < d[d][n][s: 25]]s]

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Explanation of the ungolfed code:

f: func[b][                                            ; a block of blocks of booleans
    s: 0                                               ; sets sum to 0
    foreach c b[                                       ; for each row of booleans 
        d: 0 foreach e c[if e = 1[d: d + 1]            ; count the number of 1s         
        i: find c 1                                    ; the index of the first 1
        n: either i[pick [7 9 8 5 11 12 6 3 10 4 1 2]  ; if there is 1, pick the number
                    index? i][0]                       ; at the index of 1
                                                       ; otherwise 0  
        if 50 < s: s + either 1 < d[d][n][s: 25]       ; if there is only one 1, add 
                                                       ; the number to the sum, otherwise
                                                       ; the number of 1s 
                                                       ; if the sum > 50, reset it to 25 
    ]
    s                                                  ; return the sum 
]

Answer 13

JavaScript (ES6), 98 bytes

a=>a.map(b=>b.map((m,i)=>(c+=m,d+=m*('0x'+'7985bc63a412'[i])),c=d=0)|(t+=c>1?c:d)>50?t=25:0,t=0)|t

Test cases:

f=
a=>a.map(b=>b.map((m,i)=>(c+=m,d+=m*('0x'+'7985bc63a412'[i])),c=d=0)|(t+=c>1?c:d)>50?t=25:0,t=0)|t

console.log(f([ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ])) // 0
 
console.log(f([ [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ])) // 2
 
console.log(f([ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ])) // 12

console.log(f(
[ [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ] ]
)); // 16

console.log(f(
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
  [ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1 ],
  [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] 
])); // 18

console.log(f(
[ [ 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1 ],
  [ 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ] ] 
)); // 29

console.log(f(
[ [ 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1 ],
  [ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] 
))  // 34
 
console.log(f( 
[ [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
  [ 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
  [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ] ] 
))  // 28
 
console.log(f( 
[ [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0 ],
  [ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0 ],
  [ 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1 ],
  [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ] ] 
))  // 25

console.log(f(
[ [ 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1 ],
  [ 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1 ],
  [ 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1 ],
  [ 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1 ],
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0 ],
  [ 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ] ] 
)) // 25
 
console.log(f(
[ [ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
  [ 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
  [ 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
  [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0 ] ] 
)) // 50

console.log(f(
[ [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1 ],
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
  [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ] 
)) // 27

console.log(f(  
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
  [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
  [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
  [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
  [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
  [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0 ] ] 
)) // 30

Answer 14

Python 2, 109 105 103 bytes

c=0
for l in input():a=sum(l);c+=int('7985bc63a412'[l.index(1)],16)if a==1else a;c=(25,c)[c<51]
print c

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Alternative without a recursive function.

-2 with thanks to @Jo King

Answer 15

Stax, 37 bytes

├T<↓"♥←~;▌6»≥øF←î5░U╚_π○Q▒<│∟└ù║pε♀▀æ

Run and debug it

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Explanation

F:1"=EA5MQ9-I1%)"!s@c%1={h+}{%+}?c50>{d25}{}?    # Full program, unpacked

F                                                # Loop through every element
 :1                                              # Get indices of truthy elements
   "=EA5MQ9-I1%)"!                               # Push encoded [7,9,8,5,11,12,6,3,10,4,1,2]
                 s@                              # Swap the top 2 elements of stack and get elements at indexes
                   c%1=                          # Copy the top element, get length of array, compare to length of 1
                       {h+}{%+}?                 # If it has length of 1, add the element, otherwise add the length of the array to total
                                 c50>            # Compare total to 50, 
                                     {d25}{}?    # If it is greater, pop it off and push 25 to reset counter, otherwise do nothing

Not my best work, but it works. I'm sure there is somehting I'm missing to make it a bit shorter.