# How long should an anagram be in order to be solvable by a human?

I'm writing some puzzles for a bunch of smart friends, but I'm unsure if the puzzle is too easy or too hard. For instance, an anagram like this:

fangos theorem

Should be solvable by a human without any other hint? Or should I give a hint like:

It is a famous book, consisting of three words.

If it is still hard, how can one get to the answer below, without computers?

Game of Thrones

So how can I calibrate the difficulty of an anagram? I don't want my friends (and myself) to get frustrated.

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– Rubio
Commented Feb 23, 2019 at 10:37

The interesting thing about anagrams is how their difficulty increases rapidly with the insertion of even a single new letter. For example, a short anagram like WROC can be solved within a glance. This is because of the number of ways of ordering the letters is the factorial of the number of letters: there are $$4!=4*3*2*1=24$$ possibilities to order the four characters before, easily enough to think about and rule out the wrong ones.

However, when given something like FANGOS THEOREM, there are some 2 billion possible orderings. The length you want should depend on the experience of the solvers with anagrams in the past. I find that most of my audience (a group of a dozen or so friends) can be expected to solve an 8-letter anagram with ease, but I doubt any of them would solve yours without a clue.

Given how most anagrams are traditionally a single word, listing the number of words is an important clue. After that, it would be reasonable to assume the three words form some sort of phrase, either a proverb or media title, so I would pose it as three word phrase.

It seems you are attempting to use English words when presenting the anagram (judging by your use of THEOREM). A subtle hint I would use would be to instead provide AMONGST HEREOF. Note that the second word of the solution is already contained within the clue, even enunciated by the standard pronunciation of hereof. When considering the anagram, solvers may toy with splitting hereof into two parts, and the most obvious would give one of the answer words. One issue with this, however, is the more common word the laying across the gap, so you could re-order the words to HEREOF AMONGST.

Overall, I'd say HEREOF AMONGST with the initial clue three word phrase would be a puzzle that, while difficult, I could expect people to solve before resorting to a computer solver.

On the popular British TV gameshow, "Pointless", they often have a round that has a category and then a series of the words that fit that category in anagram form (presented as English words). In this case the anagrams are of varying difficulty, but with the presence of the given category, this gives clues to the players. The way I tend to attempt them is to think of words which I know fit the category, and then look to see if any of the presented words are anagrams of this. Therefore I believe that whilst some anagrams are very difficult, even the inclusion of a category that it fits into could be a massive help, such as

"Fantasy"