What is X
Logic
Level
2
All numbers must add up to 15 . No number can be repeated more than once. Numbers are from 1-9.
What are the possible values for X?
2,6,1,7
1,8,9,5
6,2,4,8
7,5,4,8
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1 solution
<?php
//build all 9 digit combinations (123456789 through 987654321)
$arr = range(1,9);
do{
$newarr = array();
foreach($arr as $a){
for($i=1;$i<=9;$i++){
if( !preg_match('@'.$i.'@',$a) ){
$newarr[] = $a.$i;
}
}
}
$arr = $newarr;
} while( strlen( $arr[0] ) < 9 );
//loop through the array, checking sum of each row/column/diagonal
foreach($arr as $a){
if($a[0]+$a[1]+$a[2]==15 && $a[0]+$a[3]+$a[6]==15 && $a[0]+$a[4]+$a[8]==15 && $a[1]+$a[4]+$a[7]==15 && $a[2]+$a[5]+$a[8]==15 && $a[3]+$a[4]+$a[5]==15 && $a[6]+$a[7]+$a[8]==15 && $a[2]+$a[4]+$a[6]==15){
echo $a.'<br>';
}
}
?>
The code above tells me that these are all of the possible ways to solve this puzzle, noting that every solution begins with an even number
276951438
294753618
438951276
492357816
618753294
672159834
816357492
834159672