We have a winner for this seventh contest. Congratulations, Brent Yorgey! I'm delighted that Brent, of Math Less Traveled, won this one because Brent gives so much to students and readers of his blog. Brent - Enjoy your $25 gift certificate from our kind sponsor for this contest, the Art of Problem Solving.
Click here to see Brent's solution, two of them actually.
1. We received 31 submissions. Of those 23 were correct.
2. I discovered the problem here.
3. The correct answer was 25. 15 was a popular wrong answer.
4. People who didn't read the problem carefully enough - no I wasn't trying to trick people - didn't get the indexes correctly associated with the terms of the Fibonacci series. That tripped some people up.
5. Brent was one of very few people to demonstrate, via a computer program, that his answer seemed feasible. There was enough algebra in this problem that I would highly recommend that everyone compute some of the terms of the sequence numerically to get a warm fuzzy that your algebra was correct. Although, if you got tripped up with the indexes then numerical approximation would not have helped.
6. Brent used a generating function in his first solution and he did some algebraic manipulation for his second approach. A third approach that some people used was to use the closed form of the terms of the Fibonacci sequence. Ming Han's solution illustrates this approach.
Check out Blinkdagger on Monday for the next Monday Math Madness contest at Blinkdagger.