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Page for Paige

Consider this dialogue from a 2006 Foxtrot cartoon by Bill Amend:

Paige is sitting at a desk and reading from a paper, while her brother Peter listens...

Frame One
Paige: "A math teacher offers to assign one second of homework the first week of school. two seconds the second week, four seconds the third, and so on."

Frame Two
Paige: "If the amount of homework doubles every week, is this something you would agree to for the duration of the 36-week school year?

Frame Three
Paige: "I'm a little worried about answering this one wrong."

Peter: "Is that Mr. Thompson? He's evil."

Your Question #1: What is the length of the homework assignment in the 36th week?

Your Question #2: What is the average length of a homework assignment per week over the 36-weeks?


Hint: Write down the homework time for first five weeks...look for patterns.


Solution Commentary: For a similar problem, consider the Wheat and Chessboard Dilemma.