It needs Java, which you may download from here:
https://java.com/en/download/

Regards, Joe

Either that or your security settings are preventing Java from running:  https://support.mozilla.org/en-US/questions/1042240

I didn't see anything in the page source that said it was a Java plugin, only Javascript.  How did you know it was Java that was missing?

But now that I've installed Java, as you suggested, the app place holder says to "Activate Java." So now, the "Allow" button pops up. (see attached screen capture.) Do you know, is that a built-in Firefox security app?

Nonetheless, after adding in Firefox a security exception for the website, I'm still getting a security message (different from the one Joe got, nothing about a 2nd domain) and the app won't run.

I added the exception to the Java console as suggested. Now I am getting the warning about the separate domain. (See attachment.)

Question: Do you know where the "Allow" information is stored? Is it in cookies? Or is it elsewhere?

I am going to award points to this question and find another chess site on which to practice solving puzzles. This one looks good: http://www.365chess.com/puzzles.php

> Now I am getting the warning about the separate domain. (See attachment.)

The message says that the https site is in the exceptions list, but it's complaining about the jar file at the http site being on a different domain, so make sure all four of these are in the exceptions list:

http://www.TheChessWebsite.com/
https://www.TheChessWebsite.com/
http://www.TheChessWebsite.com/easypuzzle1/
https://www.TheChessWebsite.com/easypuzzle1/

If it still doesn't work after that, I'd say your idea to find other sites is the best way forward.

> Do you know where the "Allow" information is stored? Is it in cookies? Or is it elsewhere?

Probably in the permissions.sqlite file in your Firefox profile, but I'm not sure about that. This support article may (or may not) help:
https://support.mozilla.org/en-US/kb/permissions-manager-give-ability-store-passwords-set-cookies-more

> I am going to award points to this question

Thanks for that — very nice of you!

> find another chess site on which to practice solving puzzles

Yes, good idea!

> This one looks good: http://www.365chess.com/puzzles.php

I'm not familiar with it, but at least it came right up when I clicked on the link. :)

This chess wiki site that I participate in may interest you:
http://chessprogramming.wikispaces.com

It is not a puzzle site, but there are some puzzles of sorts that folks use to test their chess programs, such as this:
http://chessprogramming.wikispaces.com/R%C3%A9ti+Endgame+Study

Perusing the site may lead you to some interesting puzzles, although a Google search may be the best bet, as is often the case these days. Regards, Joe