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Problem of the Day #287: Taxes in Albertland December 31, 2011

Posted by Saketh in : potd , trackback

Alex decides to spend a year ($365$ days) in Albertland, a country with some very unusual fiscal policies. He pays his taxes in the form of one coin each day, with coins in Albertland having values of $1$, $2$, $3$, $4$, or $5$ alberts.

The government asks for a certain denomination of coin each day. However, once Alex pays a coin of value $n$, he is exempt from paying another coin of the same value for the next $n$ days, even if the government asks for one. How many distinct totals could Alex pay for that year?

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