List questions from contest-math

Published on 25 Mar 2026 - 7:50

104

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For how many values of $x$ in $0 \le x < 2\pi$ does $\frac{\sin(5x)}{\sin(x)} - \frac{\cos(5x)}{\cos(x)}=2$?

Published on 25 Feb 2018 - 10:52

565

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Killing Flies with a Checkerboard Flyswatter

Published on 25 Mar 2026 - 2:47

612

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finding sum of entries in magic square directly

Published on 22 Mar 2026 - 19:33

149

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Ratio of the area of a triangle and the area of a square containing it

Published on 27 Feb 2018 - 3:06

175

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Question from the British Mathematical Olympiad

Published on 22 Mar 2026 - 10:52

1.3k

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A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Published on 25 Mar 2026 - 5:00

109

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Circular geometry problem

Published on 25 Mar 2026 - 12:45

63

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Prove that for any $a, b, c>0$ we have:

Published on 28 Feb 2018 - 14:43

120

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Tricky Contest Problem

Published on 28 Feb 2018 - 17:53

67

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Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$

Published on 25 Mar 2026 - 9:29

408

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$n,p \in \mathbb{N}$ , $p$ prime and $1+np$ perfect square $\implies n+1$ is the sum of $p$ perfect squares.

Published on 25 Mar 2026 - 4:43

201

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Putnam 1957, 17th Problem

Published on 28 Feb 2018 - 18:52

281

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New strategy for proving an inequality

Published on 01 Mar 2018 - 14:07

156

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If $a^3+b^3=c^3,$ prove that

Published on 02 Mar 2018 - 12:17

List Question

Evaluate $(-\sqrt3 + i)^9$

For how many values of $x$ in $0 \le x < 2\pi$ does $\frac{\sin(5x)}{\sin(x)} - \frac{\cos(5x)}{\cos(x)}=2$?

Killing Flies with a Checkerboard Flyswatter

finding sum of entries in magic square directly

Ratio of the area of a triangle and the area of a square containing it

Question from the British Mathematical Olympiad

A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Circular geometry problem

Prove that for any $a, b, c>0$ we have:

Tricky Contest Problem

Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$

$n,p \in \mathbb{N}$ , $p$ prime and $1+np$ perfect square $\implies n+1$ is the sum of $p$ perfect squares.

Putnam 1957, 17th Problem

New strategy for proving an inequality

If $a^3+b^3=c^3,$ prove that

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