You have made it to the final round of the rebooted 1950’s game show, “Take-A-Chance” and because of your unbelievable luck, you have so far amassed $100,000,000 in winnings! For the final round, the game show wheels out a giant machine consisting of 6 boxes (labeled 1 through 6), each containing $1. The emcee explains that you can “spend” $1 from a given box, say box i, and choose for the game show to either:

      a) place $2 in box i+1, or

      b) interchange the contents of boxes i+1 and i+2.  

You can repeat the above as many times as possible. The emcee next gives you the following choice: you can either quit the game now and keep your $100,000,000 or, you can forfeit these previous winnings, and instead play this last game keeping all the money you generate from its play.

What should you do?