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Problem of the Week |
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PROBLEM 254 Due
to the upcoming Thanksgiving break, this problem will remain posted for
two weeks. Thanks to all for your wonderful solutions.
A mother has five children and four cookies. She wants to distribute the cookies among her children so that each child receives exactly the same amount of cookie -- both in size and shape. She has only one knife and is confident only in being able to cut a cookie-piece in half. She first cuts each cookie in half, making eight half-cookies. She gives each child one of the half-cookies and has three half-cookies left. Then she cuts each of these half-cookies in half again, making six quarter-cookies. She gives each child one of these quarter-cookies, and has one quarter-cookie left. She cuts this in half and then in half again, making eight sixteenth-cookies with which she repeats the procedure. In general, she cuts each of her cookie-pieces in half (and in half again if needed) until she has enough cookie-pieces to distribute evenly to her children, and is left with some remaining pieces for further bisection and distribution. If carried out indefinitely, will each child get 4/5'ths of a cookie? Please explain your answer. You are visitor
number
1958
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