Working Backwards: In many multiple-choice formats, plugging in answers is a viable strategy. However, since MATHCOUNTS is free-response, students must instead use "logical backtracking"—assuming a property is true and seeing if it creates a contradiction.
What is the probability that a randomly chosen letter of the English alphabet is in the word MATHEMATICS ? Express your answer as a common fraction. Count unique letters:
: This round strictly tests mental agility and paper-and-pencil calculations. Mathcounts National Sprint Round Problems And Solutions
To understand the challenge, it's best to look at some actual problems from past competitions. Here is a selection that illustrates the range of skills required.
Problem 3: Combinatorics / Probability (Targeted National Level Difficulty) Express your answer as a common fraction
Problem (Mock National Level):A bag contains 5 red marbles and 5 blue marbles. If three marbles are drawn at random without replacement, what is the probability that at least two are red?
It was a typical Saturday morning for the top mathletes in the country, gathered at the prestigious Mathcounts National Competition. The air was buzzing with excitement as they prepared for the Sprint Round, the most challenging and thrilling part of the competition. Here is a selection that illustrates the range
70+7AD2=(64⋅2)+(25⋅5)70 plus 7 cap A cap D squared equals open paren 64 center dot 2 close paren plus open paren 25 center dot 5 close paren
BA2=BD×BKcap B cap A squared equals cap B cap D cross cap B cap K is the second intersection point on line BCcap B cap C
What is the sum of the interior angles of a triangle?