Monthly Archives: August 2023

MATHCOUNTS Exercises

Posted on August 27, 2023 by kevin

Two dices are thrown simultaneously. The probability that the sum of the two numbers on the top faces of the dices is a prime number is __________. Suppose $ABCD$ is a regular triangular pyramid, with each face as a unit … Continue reading →

Posted in Math Classes, MATHCOUNTS | Comments Off on MATHCOUNTS Exercises

MathCounts Training – Number Theory – 2

Posted on August 25, 2023 by kevin

________ In base $b$, $441_b$ is equal to $n^2$ in base 10, and $351_b$ is equal to $(n-2)^2$. What is the value of $b$, expressed in base 10? ________ The base-three representation of $0.\overline{12}$ is equivalent to what base-ten common … Continue reading →

Posted in Math Classes, MATHCOUNTS, Number Theory | Comments Off on MathCounts Training – Number Theory – 2

MathCounts Training – Number Theory – 1

Posted on August 18, 2023 by kevin

________ Some positive integers have exactly four positive factors. For example, 35 has only 1, 5, 7, and 35 as its factors. What is the sum of the smallest five positive integers that have exactly four factors. ________ What is … Continue reading →

Posted in Math Classes, MATHCOUNTS, Number Theory | Comments Off on MathCounts Training – Number Theory – 1