Trainings

The table contains tennis training schedule for Saturday's younger students during the winter indoor season. Before the start of the summer season is preparing a new training schedule. Tomas Kucera will be able to practice only in the morning, sisters Kovacova will have to train in any order only one after one. Other students meet all times.

How many different schedules tennis training under these conditions can be created for these eight students?

9:00 to 9:55 Jana Abrahámová

10:00 to 10:55 Tomas Kucera

11:00 to 11:55 Beata Gross

12:00 to 12:55 Dana Ihringová

13:00 to 13:55 Ingrid Hájková

14:00 to 14:55 Katarina Kovacova

15:00 to 15:55 Zuzana Kovacova

16:00 to 16:55 Peter Valent

Correct result:

x =  4080

Solution:

Program in PHP:

for($a=1;$a<=8;$a++) {
    for($b=1;$b<=8;$b++) {
        for($c=1;$c<=8;$c++) {
            for($d=1;$d<=8;$d++) {
                for($e=1;$e<=8;$e++) {
                    for($f=1;$f<=8 ;$f++) {
                        for($g=1;$g<=8;$g++) {
                            for($h=1;$h<=8;$h++) {

if($a != 1 && $b != 1 && $c != 1)
{
    continue;
}

if($a==2 && $b!=3 || $b==2 && $c!=3
    || $c==2 && $d!=3 || $d==2 && $e!=3 ||
    $e==2 && $f!=3 || $f==2 && $g!=3 ||
    $g==2 && $h!=3)
{
    continue;
}

$aa = array($a, $b, $c, $d, $e, $f, $g, $h);
if(count($aa) != count(array_unique($aa)))
{
    continue;
}
$cnt++;

}}}}}}}}
echo 'count of permutations: '.$cnt;

$$\begin{gathered} MAX=8!=40320 \\ x=????=4080 \end{gathered}$$

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