The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

Let the set $$S=\{2,4,8,16, \ldots, 512\}$$ be partitioned into 3 sets $$A, B, C$$ with equal number of elements such that $$\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}$$ and $$\mathrm{A} \cap \mathrm{B}=\mathrm{B} \cap \mathrm{C}=\mathrm{A} \cap \mathrm{C}=\phi$$. The maximum number of such possible partitions of $$S$$ is equal to:

60 words can be made using all the letters of the word $$\mathrm{BHBJO}$$, with or without meaning. If these words are written as in a dictionary, then the $$50^{\text {th }}$$ word is:

There are 5 points $$P_1, P_2, P_3, P_4, P_5$$ on the side $$A B$$, excluding $$A$$ and $$B$$, of a triangle $$A B C$$. Similarly there are 6 points $$\mathrm{P}_6, \mathrm{P}_7, \ldots, \mathrm{P}_{11}$$ on the side $$\mathrm{BC}$$ and 7 points $$\mathrm{P}_{12}, \mathrm{P}_{13}, \ldots, \mathrm{P}_{18}$$ on the side $$\mathrm{CA}$$ of the triangle. The number of triangles, that can be formed using the points $$\mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{18}$$ as vertices, is: