Old Math

I have been reading Martin Gardner's "The Colossal Book of Mathematics" which is a collection of topics from his very long career as a writer about interesting mathematical oddities. Gardner's books are a wonderful source of material for teachers looking to challenge, perplex or intrigue students with an aptitude for math.

Here is a (paraphrased) paradox from the book:

One Friday the principal at school announces over the PA system that there will be a fire drill next week. It will be at 10 AM but in order to make the drill more authentic it will be a surprise. The principal (like all principals) is completely honest - there will be a fire drill and it will be a surprise.

Can we determine, logically, what day the drill will take place? If Friday of next week comes around and there has been no fire drill then everyone in the school will know there is going to be a drill and thus it will not be a surprise. Thus Friday is out.

On Thursday morning we know, from the previous argument, that the drill will not be held on Friday, therefore it must be held today. It will not be a surprise and thus Thursdays is not the day of the drill.

On Wednesday morning, we know that Friday and Thursday are not the day of the drill so that means today must be the day, which means it won't be a surprise… You get the idea; we can logically show that the fire drill cannot happen on any day of the week.

It is a very simple paradox to explain, yet it is a non-trivial problem, Gardner has three full pages in the bibliography on this one paradox!

I will try it out on the 7th and 8th graders this week.