• So, D arrives first and sits in the second seat from the right hand end of the row.
• Then E arrives. D has to stand up while E squeezes into the last seat in the row.
• Then A arrives. She sits on the first seat of the row.
• Now B arrives and makes A stand, while he takes the second seat in.
• Finally C arrives and makes both A and B stand up while she takes her seat.

Warm-up

Try out this situation from different starting points using scraps of paper labeled A, B C, D and E until you can see what is happening.
What is the most awkward situation you can devise?
Draw it below:

Here are four movie theater situations:

1. Place the four situations in order of "awkward-ness."
   Which is the easiest situation for people?
   Which is the most awkward?
   Explain how you decided.
   

   
   

   
   

   
   

   
   

2. Invent a way of measuring "awkward-ness." This should give a number to each situation. Explain carefully how your method works.

   
   

   
   

   
   

   
   

3. Show how you can use your measure to place the four situations in order of "awkward-ness." Show all your work.

   
   

   
   

   
   

   
   

4. Adapt your measure so that the minimum value it can take is 0 (where no-one is made to stand up) and the maximum it can take is 1 (the most awkard situation possible).

   
   

   
   

   
   

   
   

5. Show how your measure in part 4 may be generalised for any number of people entering a row. ( That is when n people enter a row with n available seats).