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• 18 Each person has at most 3 enemies in a group. Show that we can separate them into two groups where a person will have at most one enemy in the group.
• 16 Show that an orthogonal group is a $ \frac{n(n−1)}2 $-dim. $ C^{\infty} $-Manifold and find its tangent space
• 15 Show that $x^{8}+5x^{2}=1$ has exactly $2$ real roots
• 13 Composition of Derangements
• 13 Coloring 5 Largest Numbers in Each Row and Column Yields at Least 25 Double-Colored Numbers
• 11 $l^\infty(I)$ and $l^\infty(J)$ isometrically isomorphic with $|I| \not= |J|.$
• 10 Traveling Salesman Variant - Greedy Algorithm based on Least Cost better than that based on Highest
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