[You might want to check out the first two posts in the thread before going on]
George Polya uses a wide range of example in How To Solve It, ranging from some relatively advanced math problems to basic puzzles.
This example of the latter might make an interesting problem to do as a class. Here's how I'd set it up.
1. For the opening, you can pretty much just stick with what Polya has here.
2. Then have the class come up with words using at least some of the letters in the anagram.
3. You'll probably end up with relatively few words using X (and maybe Y). If so, suggest that since words with X (or X and Y) are fairly rare, it might be a good idea to list all of these the class can think of. Note that Polya gave the similar advice.
4. If the class comes up with the word EXTRA then loses steam, you might ask if there are any words that start with EXTRA.
5. If you run out of time and hints and if you can call up the internet, "when I Googled 'anagram solver' this is what I got" and go here. Remind them that finding an answer online or in a book is yet another problem solving strategy.