I don't think you understand how all this works. You're having PHP output a session variable into a text box and expecting that that text box will somehow magically update your session. Somewhere you have to pass that data back to PHP and update it. So let's make your code into a process
<?php session_start(); ?>
<form method="post" action="process.php">
Enter a number: <input type="number" name="num1" min="1" max="20" value="<?php echo $_SESSION["$num1"];?>">
<input type="submit" name="select" value="select">
</form>
What I've done is make this form do a basic POST. If you want to avoid this you can use AJAX instead (same result using JS instead of HTML)
Next, let's make a basic process.php
intermediate page
<?php
session_start();
$_SESSION['num1'] = (int)$_POST['num1'];
header('Location: 2ndpage.php');
Now we have a logistics chain for the data. You accept the data in your HTML and POST it to this page. It then takes it, sanitizes it (note I cast it to an (int)
so we are certain this is a number) and then issues a redirect to the browser which takes you to your original landing page, which should now work.
This is all oversimplified for the process of teaching. You could have your form submit directly to 2ndpage.php
and process there. Or, as I said before, you could use AJAX to send to process.php
and when it returns some success parameter you then use JS to redirect. You have many options here.