Mathcounts National Sprint Round Problems And Solutions !!hot!! Jun 2026

Coordinate geometry is your friend when no calculator is allowed. Shoelace is fast and accurate.

The is widely considered the most intense 40 minutes in middle school mathematics. As the first phase of the national competition, it sets the stage for crowning the national champion. Format and Scoring Mathcounts National Sprint Round Problems And Solutions

How many positive integers less than 100 have exactly 4 positive factors? Coordinate geometry is your friend when no calculator

( a ) is 1–9, ( b ) and ( c ) are 0–9. Minimum: ( a=1,b=0,c=0 \rightarrow 10 ). Maximum: ( a=9,b=9,c=9 \rightarrow 90+99+9=198 ). So ( 10 \le k^2 \le 198 ) → ( k ) = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. (since 3²=9 too small, 14²=196 ≤198, 15²=225>198). As the first phase of the national competition,

Calculators are strictly prohibited.Points are awarded only for correct answers.There is no penalty for incorrect guesses.The problems generally increase in difficulty as the round progresses.