Monthly Archives: January 2020

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 →

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MATHCOUNTS Exercises – 18

Posted on January 30, 2020 by kevin

How many 4-digit integers between 1000 and 9999 have their digits in non-decreasing order, such as 3447? Click here for solutions. Solution 1 – Brute Force Denote $f(m, n)$ as the number of $m$-digit integers with their digits in non-decreasing … Continue reading →

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Crazy Jumping Frog

Posted on January 29, 2020 by kevin
Posted in Algebra, Probability | Comments Off on Crazy Jumping Frog

MATHCOUNTS Exercises – 17

Posted on January 28, 2020 by kevin

In rectangle $ABCD$, shown here, point $M$ is the midpoint of side $BC$, and point $N$ lies on $CD$ such that $DN:NC=1:4$. Segment $BN$ intersects $AM$ and $AC$ at points $R$ and $S$, respectively. If $NS:SR:RB=x:y:z$, where $x$, $y$ and … Continue reading →

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MATHCOUNTS Exercises – 16

Posted on January 26, 2020 by kevin

A semicircle and a circle are placed inside a square with sides of length 4 cm as shown. The circle is tangent to two adjacent sides of the square and to the semicircle. The diameter of the semicircle is a … Continue reading →

Posted in Circles in a Square, Geometry, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises – 16