[*]All four integers must be used
[*]Each integer may only be used once
[*]Only the basic math operators +, -, *, / and parentheses ( and ) are allowed
[*]The formula must conform to standard math rules, thus for example 3 / 2 = 1.5 or 1 / 3 = 0.3 period (0.333333....).

[*]The formula must conform to the math rules of precedence (for example * before +)

[*]Some combinations can result in multiple solutions, only one is to be returned

[*]Some combinations may not result in a valid solution, then an empty string is to be returned

code:

---

$outputstring=Game24($digit1,$digit2,$digit3,$digit4)

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code:

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$out = Game24(1,2,3,4)

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code:

---

$out = '(1+2+3)*4'

---

code:

---

$out = '1*2*3*4'

---

code:

---

BREAK ON

DIM $rc, $out, $result, $i1, $i2, $i3, $i4

$rc=SETOPTION('Explicit','ON')
$rc=SETOPTION('NoVarsInString','ON')
$rc=SRND(@MSECS)


? 'Game24 KiXtart Golf running under KiXtart v'@KIX
? ''

$i1=1
$i2=2
$i3=3
$i4=4
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
$out=Game24($i1,$i2,$i3,$i4)
if trim($out)=''
  ? 'Incorrect answer, there is a solution to this combination'
  ? ''+$out+' <> 24'
else
  ? 'Please doublecheck your solution to guarantee a correct result'
  ? ''+$out+' = 24'
endif
? ''

$i1=2
$i2=2
$i3=6
$i4=8
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
$out=Game24($i1,$i2,$i3,$i4)
if trim($out)=''
  ? 'Incorrect answer, there is a solution to this combination'
  ? ''+$out+' <> 24'
else
  ? 'Please doublecheck your solution to guarantee a correct result'
  ? ''+$out+' = 24'
endif
? ''

$i1=4
$i2=4
$i3=6
$i4=6
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
$out=Game24($i1,$i2,$i3,$i4)
if trim($out)=''
  ? 'Correct answer answer, there is no solution to this combination'
else
  ? 'Incorrect answer, there is no solution to this combination'
endif
? ''

$i1=3
$i2=3
$i3=8
$i4=8
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
$out=Game24($i1,$i2,$i3,$i4)
if trim($out)=''
  ? 'Incorrect answer, there is a solution to this combination'
  ? ''+$out+' <> 24'
else
  ? 'Please doublecheck your solution to guarantee a correct result'
  ? ''+$out+' = 24'
endif
? ''

$i1=RND(9)
$i2=RND(9)
$i3=RND(9)
$i4=RND(9)
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
$out=Game24($i1,$i2,$i3,$i4)
if trim($out)=''
  ? 'No solution found'
  ? ''+$out+' <> 24'
else
  ? 'Please doublecheck your solution to guarantee a correct result'
  ? ''+$out+' = 24'
endif
? ''


$i1=3
$i2=4
$i3=7
$i4=7
$out=Game24($i1,$i2,$i3,$i4)
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
if trim($out)=''
  ? 'Incorrect answer, there is a solution to this combination'
  ? ''+$out+' <> 24'
else
  ? 'Please doublecheck your solution to guarantee a correct result'
  ? ''+$out+' = 24'
endif
? ''

$i1=1
$i2=2
$i3=8
$i4=9
$out=Game24($i1,$i2,$i3,$i4)
? 'Numbers = '+$i1+', '+$i2+', '+$i3+', '+$i4
if trim($out)=''
  ? 'Incorrect answer, there is a solution to this combination'
  ? ''+$out+' <> 24'
else
  ? 'Please doublecheck your solution to guarantee a correct result'
  ? ''+$out+' = 24'
endif
? ''

function game24($a,$b,$c,$d)
endfunction

---

code:

---

for $b=0 to ubound($a)
  if $a[$b]>0
    $c=$c+1
  endif
next

---

code:

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(1+3)*(2+4)=24
(3+1)*(2+4)=24
(3+1)*(4+2)=24

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I've been playing around with it yesterday during my class and I believe it all boils down to four generic formulas. However, you're welcome to code all 5040 unique permutations