![\[\mathcal{P}(x) = x^{108}+x^{102}+x^{96}+2x^{54}+3x^{36}+4x^{24}+5x^{18}+6\]](http://latex.artofproblemsolving.com/e/b/2/eb28918359848dd07784a3c2c6a34b934743c016.png)
be 
.![\[\dfrac{r_1^6+r_2^6+\dots+r_{108}^6}{r_1^6r_2^6+r_1^6r_3^6+\dots+r_{107}^6r_{108}^6}\]](http://latex.artofproblemsolving.com/3/1/5/315341a7adf35bc04e40ee0685a011c9f7b76115.png)
without Newton Sums.
, where 
it is positiv ,integer number.
Y by
Suppose 
die is laid down on an infinite grid of 
squares. The die starts perfectly aligned in one of the square of the grid with the 
facing up and the 
facing forward. The die can be "rolled" along an edge such that is moves exactly one unit up, down, left, or right and rotates 
correspondingly in that axis.
Determine, with proof, all possible squares relative to the starting square for which it is possible to roll the die to that square and have it in the same orientation ( facing up and facing forward).
(This problem may be hard to visualize/understand. If you don't understand the question, please ask and I can clarify.)
die is laid down on an infinite grid of 
squares. The die starts perfectly aligned in one of the square of the grid with the 
facing up and the 
facing forward. The die can be "rolled" along an edge such that is moves exactly one unit up, down, left, or right and rotates 
correspondingly in that axis.Determine, with proof, all possible squares relative to the starting square for which it is possible to roll the die to that square and have it in the same orientation (
facing up and facing forward).(This problem may be hard to visualize/understand. If you don't understand the question, please ask and I can clarify.)
