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Explore the Back-StoryHere are the questions asked in Regional Math Olympiad 2017 and their solutions. Try to solve it first and then see the solutions.

**Looking for just the problems? Download the PDF here.**

**RMO 2017, Problem 1:**

Let AOB be a given angle less than \( 180^o \) and let P be an interior point of the angular region determined by \( \angle AOB \) . Show, with proof, how to construct, using only ruler and compass, a line segment CD passing through P such that C lies on the ray OA and D lies on the ray OB and CP:PD = 1:2.

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**RMO 2017, Problem 2:**

Show that the equation $$ a^3 + (a+1)^3 + (a+2)^3 + (a+3)^3 + (a+4)^3 + (a+5)^3 + (a+6)^3 = b^4 + (b+1)^4 $$ has no solutions in integer a, b.

Written solution

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**RMO 2017, Problem 3:**

Let

**RMO 2017, Problem 4:**

Consider

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**RMO 2017, Problem 5:**

Let

Written solution part 1

Written solution part 2

**RMO 2017, Problem 6:**

Let x, y, z be real numbers, each greater than 1. Prove that

$\frac{x+1}{y+1}$ + $\frac{y+1}{z+1}$ + $\frac{z+1}{x+1}$ $\leq$ $\frac{x-1}{y-1}$ + $\frac{y-1}{z-1}$ + $\frac{z-1}{x-1}$.

Written solution

~ Discussion by Souvik Mondal & Writabrata Bhattacharya (Associate Faculty - Cheenta)

Here are the questions asked in Regional Math Olympiad 2017 and their solutions. Try to solve it first and then see the solutions.

**Looking for just the problems? Download the PDF here.**

**RMO 2017, Problem 1:**

Let AOB be a given angle less than \( 180^o \) and let P be an interior point of the angular region determined by \( \angle AOB \) . Show, with proof, how to construct, using only ruler and compass, a line segment CD passing through P such that C lies on the ray OA and D lies on the ray OB and CP:PD = 1:2.

Watch

**RMO 2017, Problem 2:**

Show that the equation $$ a^3 + (a+1)^3 + (a+2)^3 + (a+3)^3 + (a+4)^3 + (a+5)^3 + (a+6)^3 = b^4 + (b+1)^4 $$ has no solutions in integer a, b.

Written solution

Watch

**RMO 2017, Problem 3:**

Let

**RMO 2017, Problem 4:**

Consider

Watch

**RMO 2017, Problem 5:**

Let

Written solution part 1

Written solution part 2

**RMO 2017, Problem 6:**

Let x, y, z be real numbers, each greater than 1. Prove that

$\frac{x+1}{y+1}$ + $\frac{y+1}{z+1}$ + $\frac{z+1}{x+1}$ $\leq$ $\frac{x-1}{y-1}$ + $\frac{y-1}{z-1}$ + $\frac{z-1}{x-1}$.

Written solution

~ Discussion by Souvik Mondal & Writabrata Bhattacharya (Associate Faculty - Cheenta)

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