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International mathematics olympiad solutions

score 1.2k · Answer 1 · 2019-01-20 17:49:51

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International mathematics olympiad solutions

Published on 20 Jan 2019 - 17:49

score 81 · Answer 2 · 2026-03-25 09:28:37

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Determining the value of $\frac{BC}{CE}$ in a cyclic pentagon $ABCDE$.

Published on 25 Mar 2026 - 9:28

score 71 · Answer 3 · 2019-01-21 15:40:15

71

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If $abc\neq 0$, then at least one of $ax^2+2bx+c$, $bx^2+2cx+a$, $cx^2+2ax+b$ has root

Published on 21 Jan 2019 - 15:40

score 75 · Answer 4 · 2019-01-21 16:41:08

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What is the value of $a$ where $√a$ is area of a trapezoid which touches the circle with center $O$ (diameter is 2)?

Published on 21 Jan 2019 - 16:41

score 272 · Answer 5 · 2019-01-21 21:11:23

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In square $ABCD$ with side $1$, points $E$, $P$, $F$ are the midpoints of $AD$, $CE$, $BP$. What is the area of $\triangle BFD$?

Published on 21 Jan 2019 - 21:11

score 203 · Answer 6 · 2026-03-26 11:18:15

203

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How to prove using AM-GM $ \frac{4}{abcd} \ge \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} $

Published on 26 Mar 2026 - 11:18

score 4k · Answer 7 · 2019-01-22 03:23:09

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Find the numerical value of this expression

Published on 22 Jan 2019 - 3:23

score 335 · Answer 8 · 2019-01-23 13:35:44

335

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What is the minimum time needed for Shubrata and Amlan to eat 252 jackfruits?

Published on 23 Jan 2019 - 13:35

score 140 · Answer 9 · 2019-01-23 15:19:10

140

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Math competition problem involving ratios of areas. What's a good way to attack similar problems?

Published on 23 Jan 2019 - 15:19

score 527 · Answer 10 · 2026-03-27 07:17:10

527

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The number of prime pairs of $x^2-2y^2=1$

Published on 27 Mar 2026 - 7:17

score 221 · Answer 11 · 2026-02-23 03:01:18

221

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Stapled sequences- set of consecutive positive integers such that no one of them is relatively prime with all of the others

Published on 23 Feb 2026 - 3:01

score 2.9k · Answer 12 · 2019-01-24 04:03:25

2.9k

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Challenging probability problem (AMC 12B Problem 18) - Are the AoPS solutions incomplete/wrong?

Published on 24 Jan 2019 - 4:03

score 36 · Answer 13 · 2019-01-24 05:51:02

36

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Find the sum of $x_1+x_2+x_3$ of intercept points

Published on 24 Jan 2019 - 5:51

score 55 · Answer 14 · 2026-03-28 05:23:23

55

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Have any idea of a way to solve this equation? I don't have any software to solve this.

Published on 28 Mar 2026 - 5:23

score 447 · Answer 15 · 2026-03-25 18:50:12

447

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What is the value of $abc0ac$, a six digit perfect square number which is divisible by $5$ and $11$?

Published on 25 Mar 2026 - 18:50

List Question

International mathematics olympiad solutions

Determining the value of $\frac{BC}{CE}$ in a cyclic pentagon $ABCDE$.

If $abc\neq 0$, then at least one of $ax^2+2bx+c$, $bx^2+2cx+a$, $cx^2+2ax+b$ has root

What is the value of $a$ where $√a$ is area of a trapezoid which touches the circle with center $O$ (diameter is 2)?

In square $ABCD$ with side $1$, points $E$, $P$, $F$ are the midpoints of $AD$, $CE$, $BP$. What is the area of $\triangle BFD$?

How to prove using AM-GM $ \frac{4}{abcd} \ge \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} $

Find the numerical value of this expression

What is the minimum time needed for Shubrata and Amlan to eat 252 jackfruits?

Math competition problem involving ratios of areas. What's a good way to attack similar problems?

The number of prime pairs of $x^2-2y^2=1$

Stapled sequences- set of consecutive positive integers such that no one of them is relatively prime with all of the others

Challenging probability problem (AMC 12B Problem 18) - Are the AoPS solutions incomplete/wrong?

Find the sum of $x_1+x_2+x_3$ of intercept points

Have any idea of a way to solve this equation? I don't have any software to solve this.

What is the value of $abc0ac$, a six digit perfect square number which is divisible by $5$ and $11$?

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