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• 8 Show $\frac{\sin x_1\sin x_2\cdots\sin x_n}{\sin(x_1+x_2)\sin(x_2+x_3)\cdots\sin(x_n+x_1)}\le\frac{\sin^n(\pi/n)}{\sin^n(2\pi/n)}$, for $\sum x_i=\pi$
• 7 A hard inequality indian olympiad problem
• 6 $3\geq\sum\limits_{cyc}\frac{(x+y)^{2}x^{2}}{(x^{2}+y^{2})^{2}}$ with $x,y,z >0$
• 5 An olympiad-like inequality
• 5 If $x,y,z>0.$Prove: $(x+y+z) \left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right) \geq9\sqrt[]\frac{x^2+y^2+z^2}{xy+yz+zx}$
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