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<?php
/**
There are two rules for constructing an odd magic square
1. "top right"
2. "if the place is occupied, go one down"
**/
function solution($N) {
if ($N % 2 == 0) {
// I only know how to solve odd size magic squares for now.
// I'll have figure out even magic squares later.
return false;
}
$board = [];
$numbers = $N * $N;
for ($i = 1 ; $i <= $numbers; $i++) {
if ($i == 1) {
// top middle
$y = 0;
$x = ((int)($N / 2)); # would have add +1 but we starting with base 0
$board[$y][$x] = $i;
} else {
// check if top right is empty
$y-=1;
$x+=1;
$sy = $y < 0 ? $N - 1 : $y;
$sx = $x >= $N ? 0 : $x;
if (! isset($board[$sy][$sx])) {
// if empty - then assign number
$board[$sy][$sx] = $i;
$y = $sy;
$x = $sx;
} else {
// else go down a row.
$x-=1;
$y+=2;
$board[$y][$x] = $i;
}
}
}
// clean up sort the key correctly
for($i = 0; $i < $N; $i++) {
ksort($board[$i]);
};
ksort($board);
return $board;
}
print_r(solution(3)); // 3x3
print_r(solution(5)); // 5x5
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