# 2010-11 Mandelbrot Team Play Rd 1

Post date: Feb 10, 2011 11:28:22 PM

Here are the results for Mandelbrot Team Play. One of our team scored 24 points, which is the second highest.

Our team name is HUGE. Here's the key for comments.

**A)** Admirable solution, nicely presented.

**B)** Working backwards is a good problem solving strategy, but make sure to present solutions arguing forward from known information and facts.

**C)** Complete solution, or close enough; fine job.

**D)** The proof was difficult to decipher because of a confusing or illegible presentation, so less credit was awarded than might have been.

**E)** The paper merited few if any points, but the response was quite enjoyable to read!

**F) **The formula was either incorrect, or omitted, or perhaps not analogous to the one given in the previous part.

**G)** Your list accidentally went up to 32 instead of 31, giving a sum of 81 instead of 80.

**H) **Half the question was answered correctly; the other half was omitted or no headway was made.

**K)** Please don't refer to your work in the first part, since papers are separated during the grading process.

**L)** Fine answer, but more lengthy than necessary; it is OK to be more concise or cite previous results.

**M)** Mostly there; main ideas are correct but points deducted for missing details or too brief a proof.

**N)** Not bad; careless mistakes or a false statement tarnish an otherwise correct solution.

**O)** Omitted problem or no attempt at a proof.

**P)** Please do not refer to your proof written for another part. Include all work for a given part with that particular proof. (It is fine to quote the *result* of a previous part, however.)

**Q)** Your formula is correct; now explain how it follows from the identity presented in the first half of the problem.

**R)** On the right track or a few of the correct ideas present, so deserving of some credit.

**S)** One or more of the *b(n)* values were calculated incorrectly.

**T)** It is not true in general that *b*(*n-k*) = *b*(*n*)-*b*(*k*). The fact that *b*(31-*k*) = *b*(31) - *b*(*k*) is special and should be explained.

**U)** Your inductive step works when *n*+1 is odd, but one must also address the more difficult case where *n*+1 is even.

**V)** Your formula is correct, and you have good ideas for the first part, although it has not been completely explained.

**W)** On the wrong track or a very difficult approach, but warranting some credit.

**X)** You have shown that the equality holds for some values of *r*; now find an argument to show that it is always true.

**Y)** Little or no significant progress towards a solution (occasionally despite a fair amount of work), or misinterpretion of the question.

**Z) **Please clearly define any expressions or functions used in your formula.