Author Archives: kevin

Problem of the Day – March 15, 2020

Posted on March 15, 2020 by kevin

Let $a$ and $b$ are positive integers that makes $\dfrac{\sqrt{2}+\sqrt{a}}{\sqrt{3}+\sqrt{b}}$ a rational number, where $a <= b$. Find all pairs of $(a, b)$.

Posted in Algebra | Comments Off on Problem of the Day – March 15, 2020

MATHCOUNTS Exercises – 21

Posted on February 15, 2020 by kevin

The perimeter of rhombus $ABCD$ is 8 and its area is 2. Find the value of $\angle{ABC}$ in terms of $\pi$. Click here for the solution. Solution Draw line $AE$ perpendicular to $BC$ with $E$ on $BC$. Connect $A$ and $C$ to form two congruent $\triangle{ABC}$ and … Continue reading →

Posted in Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 21

Who is the thief?

Posted on February 3, 2020 by kevin

Four burglary suspects, A, B, C, D were summoned to the court to face the judge. When the judge asked: “Who is the thief?”, each of the suspects answered as following: A: B is the thief.B: C is the thief.C: … Continue reading →

Posted in Logic, Puzzles | Comments Off on Who is the thief?

MATHCOUNTS Exercises – 20

Posted on February 1, 2020 by kevin

Given an equilateral $\triangle{ABC}$ shown below, $AB=BC=CA=1$, point $D$ and $E$ trisect side $AB$, point $F$ and $G$ trisect side $BC$, point $H$ and $I$ trisect side $CA$. Two overlapping equilateral triangles are formed by linking various intersect points. Find … Continue reading →

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MATHCOUNTS Exercises – 19

Posted on January 31, 2020 by kevin

For the following equation $$ x\times y\times z = 360$$ Determine the number of unique positive integer solutions. Determine the number of unique integer solutions. Click here for the solutions. Solution for Question 1 Because the product of $x$, $y$ … Continue reading →

Posted in Combinatorics, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 19