Cheryl’s Birthday Problem and Information Filtering

I love seeing teasers about math and logic gain popular appeal! Here’s the math (specifically, logic) problem that the internet is talking about today:

Cheryl's birthday problem

You can get the full problem nicely presented on either The Guardian or The New York Times websites. A number of other sites are talking about it today, too. Just Google “Cheryl birthday problem.”

I spent some time with the problem and put together this response here. I know that various online outlets have discussed the answer as well; here are the respective solutions presented by The Guardian and The New York Times (don’t click those links until you think about the problem for yourself). But I think there’s a useful “information” framework to use in considering how to arrive at the answer. I discuss that framework at the end.

Spoiler alert — I’m going to discuss the birthday answer starting in the next paragraph.

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