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Problem of the Day #276: Christmas Cookies December 20, 2011

Posted by Seungln in : potd , trackback

Albert, Alex, Arjun, Billy, Mitchell, Saketh, SeungIn and Sreenath have a huge pile of Christmas cookies. They do an epic sleepover at Saketh’s house, where the cookies are. In the middle of the night, Albert wakes up and eats $1$ more than $\frac{1}{3}$ of the cookies, and goes back to bed. Later that night, Alex eats $2$ more thanĀ $\frac{1}{3}$ of the remaining cookies, and goes back to bed. Arjun gets up later, eats $3$ more than $\frac{1}{3}$ of the remaining cookies, and goes back to bed, and so on. The $n$th person eats $n$ more than $\frac{1}{3}$ of the cookies. If there are $238$ cookies remaining after each person has eaten cookies, how many cookies were there to start with?

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