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Hi all

The solution I 've adopted is different (graphic captcha) but answering to @max565 the math check have to be done before SendMessage call on ContactForm.php.

I'm using version 4.4.1 of the module in Prestashop 8.1.2, and in the code of the module I put the code

 		$mathAnswer = Tools::getValue('mathAnswer');
        $mathNumber1 = Tools::getValue('mathNumber1');
        $mathNumber2 = Tools::getValue('mathNumber2');
        $mathSum = $mathNumber1 + $mathNumber2;  

In the very beginning of the function getWidgetVariables we can see an if clause :

 public function getWidgetVariables($hookName = null, array $configuration = [])
    {
        $notifications = [];

        if (Tools::isSubmit('submitMessage')) {
			$this->sendMessage();

And there, is a good place to test the new field and return if error. Replace the line  $this->sendMessage(); with Something like:

        if (Tools::isSubmit('submitMessage')) {
            // Math test //
 			$mathAnswer = Tools::getValue('mathAnswer');
        	$mathNumber1 = Tools::getValue('mathNumber1');
        	$mathNumber2 = Tools::getValue('mathNumber2');
            if ($mathAnswer == $mathNumber1 + $mathNumber2) {
                $this->sendMessage();
            } else {
                $this->context->controller->errors[] = Tools::displayError('The answer is wrong');
            } 
...

So if "submit", test the math. If "Ok" call sendMessage()

Hope this helps.