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Problem of the Day #99: Transaction Fees June 26, 2011

Posted by Saketh in : potd , trackback

Mitchell is purchasing cookies at the local bakery. He can buy cookies one at a time: the first will cost $\$1$, the second $\$2$, and so on. That is, the $n^{\mathrm{th}}$ cookie will cost $\$n$. However, his debit card company deducts $\frac{1}{7}$ of the funds on his card before charging for any purchase.

Suppose he arrives at the bakery with an integer number of dollars on his card. If he buys some cookies and ends up with exactly $0$ dollars, what is the greatest amount of money he could have started with?

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