Problem of the day for Friday, November 9

Yesterday's problem

November 7 hints and answers

Monday is Veterans' Day, a holiday in the Philly School District. So we'll be back on Tuesday with the next Problem of the Day.

If 120 seats are arranged in a row (that is one really long row!), what is the least number of seats that must be occupied so the next person seated must sit next to someone?

It will definitely help to make a diagram like the one above, where the blue shapes represent occupied seats in the L-O-N-G row of 120 seats, and the red shapes represent unoccupied seats. (Of course, in that diagram, someone could still sit down in one of the red unoccupied seats and not be right next to anyone already in a blue seat).

You'll also find it useful to use the strategies of simplifying the problem (try a shorter row first) and looking for patterns.

As always, be sure to explain the work you did to arrive at your answers!