Problem 1:
0+
+1p for an algebraic transformation or change of variables which could
possibly lead to a solution
+2p for a division or factorization similar to the ones in the
official solution
(these points are not additive)
5-
-1p for a very minor mistake (I can't imagine what that would be)
-2p for a minor mistake which leads to not getting an integer
Problem 2:
0+
+1p for a correct solution of the case Q=B
+1p for ideas which could lead to a solution (e.g. translation into
trigonometry with the angles A,B,C only)
(additive)
5-
-1p not all cases regarded/mentioned; the case Q=B has to be solved
separately
-1p/-2p for flaws in the proof
Problem 3:
0+
Examples: +2p for an example in the case n=9
+1p for an example with n>9
Elimination: +2p for elimination of n=8
+1p for elimination of n=5,6 or 7
The points from the two groups are additive.
5-
-1p for elimination of n=8 and example for n=9, without the
observation that it is enough to eliminate n=8
Problem 4:
0+
+1p for the correct answer
+2p for a translation into the language of paths (or sets)
5-
-1p for correct answer for even n, a mistake in the answer for odd n