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Problem of the Week (POW)
POW 4
Problem of the Week - Math 340 students take note!!
There is a coin at each vertex of a regular 10-gon. Alice and Bob take turns removing one coin, with Alice going first. A coin at vertex V can be removed only if there is an acute-angled triangle with vertices at V and at two other remaining coins. A player who cannot move loses. Who has a winning strategy? Note: A 90-degree angle is not acute.
POW 3
Ok , no one was too excited about the last problem I posted, but I think you'll like this one:
This one is a kind of combination of KenKen and Sudoku except there are no clues. So let's call it Clueless SudoKen, and I will give you till after break (Tuesday, 10/18/11) to solve it. As always, prizes will be awarded.
Referring to the figure below, your job is to fill in the squares with the numbers 1 through 6 so that every row has 1 through 6, every column has 1 through 6 and that the sum of the numbers in each of the nine regions in the figure is the same.
Go for it!
POW #2
Congratulations to Wiley Radowski and Abe Lauer , the winners of last week's puzzle! Their prizes will be awarded next week and the solution will be posted outside my office door on Monday, because I forgot to do that today.
New Puzzle:
Suppose a positive integer n has divisors d(i), where
1 = d(1) < d(2) < d(3) < . . . < d(k) = n
and
d(7)^2 + d(15)^2 = d(16)^2.
What is d(17)?
Those of you who attended Sunil's talk last Thursday should notice something familiar! In fact, here's a hint:
Fact: If (x,y,z) is a Pythagorean Triple, then the product, xyz is divisible by 3, by 4 and by 5.
Your mission:
a) Prove the fact
b) Use the fact to find d(17)
Please submit your solutions to me by email or snail mail under my office door. The contest will close on Monday, 9/19
POW #1
All - The problem of the week, which was on vacation last year, has returned!
For those of you who are new, I will be sending a problem about once a cycle or so for your consideration.
There will be fun! There will be prizes! Anyone can enter, but only students can win prizes.
Send your entries to jgalovich or give to me directly. Problems will also be posted outside my office door -- PE261.
Let the fun begin!
Here is the first problem:
In the attached "railway map", find a path from A to B. You must follow the curved "tracks" as if you were a train, and you cannot go backwards. I am told there is a unique solution. Find it. 
Solutions will be accepted until Friday 9/9/11. The first legal solution is the winner.