Category Archives: MATHCOUNTS

2020 Mathcounts State Sprint Round #30

Posted on April 22, 2021 by kevin

Hank builds an increasing sequence of positive integers as follows: The first term is 1 and the second term is 2. Each subsequent term is the smallest positive integer that does NOT form a three-term arithmetic sequence with any previous … Continue reading →

Posted in Logic, MATHCOUNTS | Comments Off on 2020 Mathcounts State Sprint Round #30

MATHCOUNTS Exercise – 22

Posted on January 1, 2021 by kevin

Point $E$ and $F$ are inside the square $ABCD$, with $DE=10$, $EF=6$, $BF=4$, and $\angle{DEF}=\angle{BFE}=90^\circ$. Find the area of the square $ABCD$. Click here for the solutions. Solution 1: Draw line $DB$, intersecting $EF$ at $G$. We have $\triangle{DEG}\sim\triangle{BFG}$. $\therefore … Continue reading →

Posted in Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercise – 22

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 →

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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