You’ve probably seen the “birthday logic puzzle” that’s gone viral in the past few days. If you haven’t, you might want to try to solve it yourself. Here it is:
Two dynamic epistemic logicians, Audrey Yap (UVic) and Barteld Kooi (Groningen) explained the solution (and how to get it) on facebook. “Dynamic” here modifies “epistemic”, not “logicians:” there is something called “dynamic epistemic logic” which is used here. FWIW, I know that Audrey at least is very dynamic.
Audrey’s solution, posted with her kind permission:
These are all the possibilities at the start. The red lines represent Albert’s uncertainty, and the blue lines represent Bernard’s uncertainty. So there’s a red line between May 15 and May 16 because Albert would only know it’s May and not what date. And there’s a blue line between May 15 and Aug 15 because Bernard would only know it’s the 15th and not what month.
Then the first important piece of information is that Albert knows that Bernard doesn’t know the date. This eliminates a lot of dates, because if Albert is certain that Bernard doesn’t know the date, we can’t be in a month where Bernard might know the date. That effectively eliminates May and June, because in both of those months, there’s a possibility Bernard could already know the date.
And then the next interesting thing we learn is that, after learning that piece of information, Bernard does know the date. So here’s what it looks like with May and June eliminated and how we figure out what to do with that information. Since Bernard now knows the date, it can’t be the 14th, since then he still wouldn’t know.
Then last, when we see that Albert actually learned the date from hearing the fact that Bernard does, know there’s only one date it could possibly be. So here’s what it looks like when we eliminate the 14th as a possibility.
Barteld Kooi’s video explanation is here on facebook and also on YouTube: