Birthdays Can’t Be A Problem!

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Growing up I remember enjoying logic puzzles. The kind where you would draw a grid of all of the people and one other attribute about them to, by process of elimination, determine the solution to the posed problem. Somehow, I am no longer any good at these puzzles. Or, they have become much more complicated (or maybe I don’t remember cheating?).

Recently though I came across a Birthday Problem in the Guardian:

“Ariel, Balthazar and Chastity are great mates, genius logicians and they always tell the truth. Neither Ariel nor Balthazar know the day or the month of Chastity’s birthday, so she decides to tell them in the following way:

First, she says out loud, so both Ariel and Balthazar can hear her: “The day (of the month) of my birthday is at most the number of the month of my birthday.”

Then she whispers the day to Ariel and the month to Balthazar

Ariel says “Balthazar cannot know Chastity’s birthday.”

Balthazar thinks a bit, then says: “Ariel also cannot know Chastity’s birthday.”

They carry on like this, each saying these exact same sentences in turn until Balthazar announces: “Both of us can now know what Chastity’s birthday is. Interestingly, that was the longest conversation like that we could have possibly had before both figuring it out.”

When is Chastity’s birthday?”

I read the first few lines and thought, “this one I can do.” She has to have been born by the 12th day of the December, right? Only that still leaves me with a whole lot of options and the remaining text of the clue did not help me at all!

How does their saying to one another that they “cannot know Chastity’s birthday” over and over again get us to the answer?! Argh. This is why my brother is the logician in the family (really, truly, he is) while I’m the one blogging about birthdays.

What about you? Did you figure it out? If not, the answer is provided here. Wish I could say it made me bang my head to my forehead and say “oh, of course! How could you miss that?!” But, no, I really must have been cheating to do well on these in the past.

This isn’t even the first birthday problem I’ve encountered. Seems wrong to me to make birthdays a skill-testing question.

 

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