Tag Archives: Fermat Contest

Fermat Contest 2019 Question 17 on Equilateral triangle inscribed in Regular Pentagon

Posted on January 24, 2026 by Sumant Sumant

The five sides of a regular pentagon are all equal in length. Also, all interior angles of a regular pentagon have the same measure and is equilateral. The measure of obtuse is

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Fermat Contest 2016 Question 20 on folding paper

Posted on January 24, 2026 by Sumant Sumant

It’s a great question on how coloring can make the folded angles obvious Continue reading →

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Fermat Contest 2020 Question 23 on Functional Equation

Posted on January 20, 2026 by Sumant Sumant

There are real numbers and for which the function has the properties that for all real numbers and for all real numbers . What is the value of

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Fermat Contest 2019 Question 20 on and equilateral triangle on a circle with a radius 2

Posted on January 18, 2026 by Sumant Sumant

The vertices of an equilateral triangle lie on a circle with radius 2. What is the area of the triangle ?

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Fermat Contest 2019 Question 19 on Functional Equation

Posted on January 18, 2026 by Sumant Sumant

The function has the properties that and for every integer . What is the value of ?

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Fermat Contest 2020 Question 23 on Functional Equation

Posted on January 16, 2026 by Sumant Sumant

There are real numbers and for which the function has the properties that for all real numbers, and for all real numbers . What is the value of ?

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Fermat Contest 2020 Problem 24 on Tangential Circles

Posted on January 16, 2026 by Sumant Sumant

Note: This is a problem very similar to one given in L.A Graham’s book.

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Fermat Contest 2021 Problem 24 on circle inequality

Posted on January 16, 2026 by Sumant Sumant

A pair of real numbers (a,b) with is chosen at random. If p is the probability that the curves with equation and intersect, then 100 p is closest to ?

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Fermat contest 2021 question 18 on isosceles triangle with three lunes

Posted on January 15, 2026 by Sumant Sumant
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Fermat contest 2021 Question 19 on three simultaneous equations

Posted on January 15, 2026 by Sumant Sumant
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