Sí, con eso valdría.
Código PHP:
$f = fopen("archivo.txt", "w");
$s = fread($f, 1);
fseek($f, 0);
if($s == "A"){
fwrite($f, "B");
header("Location: A");
}else if ($s == "B"){
fwrite($f, "C");
header("Location: B");
}else{
fwrite($f, "A");
header("Location: C");
}
fclose($f);
