At the end of the year 2000, Steve had \100\. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which year did Steve have more money than Wayne for the first time?
Solution
We make a table of the total amount of money that each of Steve and Wayne have at the end of each year. After the year 2000, each entry in Steve's column is found by doubling the previous entry and each entry in Wayne's column is found by dividing the previous entry by 2. We stop when the entry in Steve's column is larger than that in Wayne's column: \begin{tabular}{|r|r|r|} Year & Steve & Wayne \\ \hline 2000 & \100 & \ \\ 2001 & \200 & \ \\ 2002 & \400 & \ \\ 2003 & \800 & \ \\ 2004 & \1600 & \ \end{tabular} Therefore, 2004 is the first time at which Steve has more money than Wayne at the end of the year.
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