"It's not that I'm so smart, it's just that I stay with problems longer." [Albert Einstein]
Mr Excel's challenge of the month of August 2002 stated:
"An accounts receivable department receives a check from a customer for $4,556.92. Upon looking in the accounting system, there are 54 unpaid invoices, ranging from $77.74 to $5,465.45. The payment must be for some exact combination of entire invoices, but we don't know which invoices are being paid."
The winning solution was published here. Michael Schwimmer presented a nice and elegant solution on his (now retired) website - in German. I translated his version into English because I found it quite beautiful.
Tushar Mehta presents a nice algorithm (which can calculate all solutions) here.