# OddThinking

A blog for odd things and odd thoughts.

### Fuzzy Hangman

Here’s an idea for a Hangman variation, that I am calling Fuzzy Hangman.

It was triggered by the Lempel-Ziv (or Lempel-Ziv-Welch, if you prefer) comment in the previous post.

Rather than a single letter, the guessing player can try a set of letters in a single turn. So, rather than asking “Is there an E?” they can ask “Is there an E, L or R?”

The player who knows the secret word should not reveal the actual letter, but instead indicate which positions in the word that there is any match in the set.

So, if the secret word is SECRET, the answer would be “Yes: the second, fourth and fifth letter.”

The guessing player might record that like so: “_ E/L/R _ E/L/R E/L/R _”.

If the next question was “Is there an E, T or N?” the answer would be “Yes: the second, fifth and sixth letter.”

The guessing player would then know this: “_ E _ L/R E T/N”.

Would this work as a game?

Well, merely counting the failed guesses wouldn’t work to decide if the guesser had won – the guessing player, once they knew there was an E present, would just always include an E in their guess, so the answer was always “Yes”. The hangman would never be drawn.

So you would need to restrict the total number of guesses, successful or otherwise.

If you allowed more than 5 or more guesses, there would be a simple and boring solution:

Guess 1: Is there any of ACEGIKMOQSUWY?
Guess 2: Is there any of ABEFIJMNQRUVYZ?
Guess 3: Is there any of ABCDIJKLQRSTYZ?
Guess 4: Is there any of ABCDEFGHQRSTUVWX?
Guess 5: Is there any of ABCDEFGHIJKLMNO?

With these questions, it is possible to determine the exact letter for each position. (How to produce and use such strings is left as an exercise to the reader.)

With only four guesses permitted, it would start to become interesting. Only three guesses would be more challenging still – it would be a bit like taking a phone number, and trying to make a word from the associated letters.

Coming up with the best letter sets to best identify the words would be an interesting challenge. Having them adapt as you learnt information would be even more challenging.

Finally, improving the word choice to ensure maximum ambiguity under such conditions would be a great challenge – I can’t predict where the Nash Equilibrium would fall. Is four guesses enough to identify any word in the dictionary? If so, how about three? Or will a canny word selection stop the guessing player from succeeding?

Another variant to consider might be to limit the number of letters per submission to, say, four.

If anyone tries it, let me know.

### Comment

1. my intuition before I even got to the end was that you’d want to limit the number of letters submitted per guess. I’ll keep this in mind if/when I play hangman again

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