John was sent out to buy some cookies.
"You'll have to give me half the cookies and also half a cookie," his mother told him, "and then you'll have to give Agnes half the remaining cookies and also half a cookie, and after that Jack will get half the balance and also half a cookie."
"Okay, Mom, but what do I get?" asked the boy.
"You know you don't like cookies," he was told, "but fix it so that there will be just one cookie left for yourself."
How many cookies did John have to buy?
Note 1: What if there had been other members of the family...Carl, June, Carol...etc. 35 members strong....and all wanted the same "half the remaining cookies and also half a cookie"...could you solve it? (i.e. look for a pattern)
Note 2: What if the problem had involved giving "one-third the remaining cookies and also one-third a cookie," is it solveable?
Source: J. Hunter, Fun with Figures, Dover, 19??
Hint: Two useful problem solving strategies here are "guess-and-adjust" and/or "working backwards."
Solution Commentary: I hope you did not resort to the superpower of algebra in solving this problem. If you did, I hope you enjoyed the complex manipulations!