As a child I loved playing “Guess who?” by MB games. If you’ve not seen it before the aim of the game is to work out your opponents character before they guess yours. You ask Yes/No questions (eg. “Do they have a hat?”) which helps you narrow down who the person is.

I used to think I was pretty good at the game and enjoyed making up variations like “Stereotype guess who?”. Asking questions like “Would they own a cat?” or “Would they be a member of Greenpeace?” or “Do they have a problem with alcohol?” It’s surprising how accurate you can be at guessing the character this way!

One day in the shower I had the crazy idea (not the first time) of wondering if it was possible to play the game blindfolded. This then led me down the route of working out both an optimal strategy and then how to memorise the characters. before I go any further, quickly have a think what would be the best strategy for a game like Guess Who?

Ideally you want to create a binary search by each question eliminating half of the characters. That way with 24 characters you are guaranteed to win in 5 questions (=Log 24 where I’m using a logarithm of base 2).

However, the game designers are wise to this and have picked the characters to thwart this. Every major character feature has a 5:19 split. There are 5 women, 5 hats, 5 glasses, 5 beards etc. So with each question there’s a small chance of being lucky and getting down to just 5 people or a much larger chance of only eliminating 5 people.

Having stared at those faces for far too long I decided the best opening question is: “Does the person have any facial hair?” as there are 8 people with beards or moustaches. Below is a chart showing the route I’d then take. You can then make up charts for the other options if there’s no facial hair. Personally I then ask if they were a women, if not then do they have glasses, if not then do they have a hat. Etc.

An alternative more efficient but less pleasing approach would be to split the characters exactly in half and ask: “Does their name start with a letter A to G?”

How would you approach the problem?

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I like this idea. I might use it later in the year. Get my year 7s to come up with the best strategy they can…

Are you allowed to ask a composite question such as “Do they have a hat, glasses or a moustache?” (these are random things – I’ve not counted how many of each there are and in what ways they overlap) so that the combination has a combined probability of a half – and then progress with a binary search in that way?

I don’t see why you can’t.