You might already be familiar with the game: Basketball FRVR in facebook. There are two types of score you can make:

  • A virgin-shot:(we call it so in our country :D) When the ball enters the basket without touching the rim or
  • A stale shot: When the ball enters the basket, but after touching the rim.

The game is over once you miss a shot. Stale shot always scores 2 points.The first in a run of consecutive virgin-shots scores 3 points, the second scores 6 points, and subsequent ones score 9 points each.

For example,

Hits             Total score 

S-V-V-V          2+3+6+9 = 20
S-V-V-V-V        2+3+6+9+9 = 29 (see how added score for consecutive virgin-
                                 saturates at the 5th hit)
S-V-S-V-V-S-V    2+3+2+3+6+2+3= 21

Using simple mathematics, it can easily be proven that any score greater than 1 n>1 can be scored in the game

The Challenge

For any given number 1<n<100, output all the possible ways to score n.


  • You can either write a complete program or function(s), snippets however are not acceptable.
  • Hard-coding the output or loading from memory/other programs/website is strictly prohibited, you must compute the output in real-time.
  • The output must be a well-separated collection of string of Ss and Vs. For eg: ['SVS','SSV','VSS'] or {'SVS','SSV','VSS'}.
  • It is encouraged to, but the collection need not be sorted or contain only unique elements. Brownie points if you output sorted and unique collection of strings.

Winning condition:

  • This is so the shortest code in bytes wins.

Input/Output (Test-cases)

2: {'S'}
3: {'V'}
4: {'SS'}

Thanks to Peter Taylor for improving this question

  • 10
    \$\begingroup\$ In case anyone cares, as an American, I always called rimless (and backboardless) shots "swishes" (and Wikipedia backs me up here: Swish, a basketball shot that goes through the basket without touching the rim or backboard) \$\endgroup\$
    – Stephen
    Jul 5, 2017 at 14:43
  • 3
    \$\begingroup\$ I'm mostly just curious where they call them 'virgin shots'... I'm afraid to look it up behind my company's firewall xD \$\endgroup\$
    – bendl
    Jul 5, 2017 at 14:49
  • \$\begingroup\$ @bendl Nepal or Npl when censored. xD \$\endgroup\$
    – 0xffcourse
    Jul 5, 2017 at 15:04
  • 1
    \$\begingroup\$ Very nice question—not hard, but definitely not trivial, and allows for different approaches :) \$\endgroup\$ Jul 5, 2017 at 17:17
  • 1
    \$\begingroup\$ I think 28 should be 29 in the second test case. \$\endgroup\$ Jul 5, 2017 at 17:34

6 Answers 6


Jelly, 30 bytes


A monadic link returning a list of the strings (lists of characters).

Try it online! - The footer calls the link and separates the entries by newlines since a full program's implicit output would smash them together.


o2,5ṁo8‘ - Link 1, helper to form shot scores: list of shots grouped by type (S=1 and V=0)
         -                                e.g. [[1,1],[0,0,0,0,0],[1,1],[0],[1,1]]
 2,5     - 2 paired with 5 = [2,5]
o        - logical or (vectorises)             [[1,1],[2,5,0,0,0],[1,1],[2,5],[1,1]]
    ṁ    - mould like the input                [[1,1],[2,5,0,0,0],[1,1],[2],[1,1]]
     o8  - logical or with 8                   [[1,1],[2,5,8,8,8],[1,1],[2],[1,1]]
       ‘ - increment                           [[2,2],[3,6,9,9,9],[2,2],[3],[2,2]]

Hṗ@€⁾VSẎðOḂŒgÇ€FS=ðÐf - Link: number, total score, n
H                     - halve n
    ⁾VS               - literal ['V','S']
 ṗ@€                  - Cartesian power with swapped @rguments for €ach
                      -   ...i.e. for each in [1,2,...,floor(half n)]
                      -   yielding all strings of Vs and Ss from length 1 to floor(half n)
       Ẏ              - tighten (from a list of lists of lists to a list of lists)
        ð         ðÐf - filter keep those entries for which this yields a truthy value:
         O            -   cast to ordinals (S->83, V->86)
          Ḃ           -   modulo 2         (S->1, V->0)
           Œg         -   group equal runs (e.g. [0,0,1,1,0] -> [[0,0],[1,1],[0]])
             Ç€       -   call the last link (1) as a monad for €ach (transform to scores)
               F      -   flatten (make one list of scores)
                S     -   sum (calculate the total score of the string)
                 =    -   equals right argument (n)?

The resulting order is actually lexicographical in reverse, to have it forward sorted just reverse it by appending .

  • \$\begingroup\$ Nice. Your brownie 🍪. \$\endgroup\$
    – 0xffcourse
    Jul 6, 2017 at 7:54
  • 1
    \$\begingroup\$ @officialaimm We usually call those cookies but whatever... \$\endgroup\$ Jul 6, 2017 at 12:00

JavaScript (ES6), 73 72 bytes

Prints all unique, lexically sorted combinations.


Test cases

In this snippet, alert() has been replaced by console.log() for user-friendliness.


;[2, 3, 4, 12, 16]
.forEach(n => { console.log('[' + n + ']'); f(n); })

  • 1
    \$\begingroup\$ Here's a crunchy brownie: 🍪 \$\endgroup\$
    – 0xffcourse
    Jul 5, 2017 at 16:02

PHP>=7.1, 158 bytes

function b($s="",$g=0){global$r,$i;$g-$i?$g>$i?:b($s."2",$g+2)&b($s.($n=$s[-1]>2?min(9,$s[-1]+3):3),$g+$n):$r[]=strtr($s,2369,SVVV);}$i=$argn;b();print_r($r);

PHP Sandbox Online


function b($s="",$g=0){
      :b($s."2",$g+2) # recursive call add a S
      &b($s.($n=$s[-1]>2?min(9,$s[-1]+3):3),$g+$n) # recursive call add a V
    :$r[]=strtr($s,2369,SVVV); # add to result array if reach score replace integers with S and V
$i=$argn; #short input variable
b(); #call the function
print_r($r); #print results
  • \$\begingroup\$ @officialaimm You must use a PHP Version equal greater than 7.1 \$\endgroup\$ Jul 5, 2017 at 15:28
  • 1
    \$\begingroup\$ @officialaimm you can change the version to the highest available version. At the first time you visit the site it is not set to a PHP 7.1 Version And the only output I reach for input=6 with a Version 7.1 is SSS \$\endgroup\$ Jul 5, 2017 at 15:39
  • \$\begingroup\$ Oh, its fine now.Anyways, its quite weird how different versions of PHP are giving different outputs for the same code though.. :D \$\endgroup\$
    – 0xffcourse
    Jul 5, 2017 at 15:43
  • 1
    \$\begingroup\$ @officialaimm This depends on the new feature in PHP 7.1 that is use in this case. $string[-1] belongs to "" in all versions under 7.1 php.net/manual/en/language.types.string.php \$\endgroup\$ Jul 5, 2017 at 15:48

Python 3, 96 95 85 77 73 bytes

-1 byte thanks to @notjagan
-4 bytes thanks to @xnor

f=lambda x,s='',i=3:f(x-2,s+'S')+f(x-i,s+'V',3*(i<9)+i)if x>0 else[s]*-~x

Try it online!

  • 3
    \$\begingroup\$ You can remove a byte by changing x==0 to x<1. \$\endgroup\$
    – notjagan
    Jul 5, 2017 at 14:40
  • \$\begingroup\$ Recursive functions that print can usually be shortened to instead produce a list. In place of printing, return a list of length 1 or 0, and recursively sum the lists corresponding to the branches. \$\endgroup\$
    – xnor
    Jul 6, 2017 at 2:54

Mathematica, 95 102 105 112 bytes


There should be a lot of golfing potential.

Bascially it is a recursive function that perform a DFS over all possible combinations.


Haskell, 75 bytes


Call f with the total score value. Uses a fairly straightforward depth-first search to find all the solutions. Sadly, Haskell's precedence rules seem to be out to get me today, so there are lots of parentheses here.

  • \$\begingroup\$ As @Laikoni pointed, VVVV should evaluate to 27 while you seem to evaluate it as 30. \$\endgroup\$
    – 0xffcourse
    Jul 6, 2017 at 8:00
  • \$\begingroup\$ Fixed the truncation problem at the cost of a few bytes. Thanks, @Laikoni, for pointing that out. \$\endgroup\$ Jul 6, 2017 at 11:59
  • 1
    \$\begingroup\$ @Laikoni If I change <$> to map, I have to wrap the # call in parentheses, so it's a wash. \$\endgroup\$ Jul 6, 2017 at 12:00

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