Now that the MMM #35 deadline has passed …

June 30th, 2009 | by Sol |

MMM #35 turned out to be harder than I thought judging by the small number of submissions I received.

I’ll be giving away four prizes on Friday - two to the early submitters, one to .mau. for consistently submitting entries to the contest for a really long time, and one to a randomly selected person with a correct submission.

I’ll discuss some of the solutions on Friday but, for now, check out these pictures I made. I came up with this problem by playing with the Fibonacci series and arranging rectangles.

Here is the problem description:

Let F(0)=1, F(1)=1, and F(n)=F(n-2)+F(n-1). This is the familiar Fibonacci series.

Simplify F(0)xF(1) + F(1)xF(2) + F(2)xF(3) + F(3)xF(4) + … + F(n-1)xF(n) + F(n)xF(n+1)

Show your work.

Can you see how these pictures help one to see why the sum is what it is? Do you see why there are two different pictures?

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  1. 3 Responses to “Now that the MMM #35 deadline has passed …”

  2. By watchmath on Jun 30, 2009 | Reply

    Nice!
    Do you have this before you know the answer to the problem or after?

  3. By Steve on Jul 1, 2009 | Reply

    Hmmm - reminds me a lot of the golden rectangle.

  4. By Sol on Jul 4, 2009 | Reply

    I can’t quite recall. I was going back and forth between the pictures and the formula.

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