Mathcounts National Sprint Round Problems And Solutions __exclusive__ -
The MATHCOUNTS National Sprint Round is the individual portion of the National Competition which consists of 30 problems to be solved in 40 minutes
Step 1 – Use divisibility rules.
For ( 5a4 ) divisible by 9: sum of digits must be multiple of 9. Digits: ( 5 + a + 4 = 9 + a ) must be divisible by 9 → ( 9+a = 9 ) or ( 18 ). So ( a = 0 ) or ( a = 9 ). Mathcounts National Sprint Round Problems And Solutions
page provides samples and recent year chapter/state rounds. National rounds are typically not released for free on the official site. AoPS Wiki: Art of Problem Solving The MATHCOUNTS National Sprint Round is the individual
Strategy: Always look for factoring patterns before brute force. Solution: Divide the total number of pieces of
Solution:
Divide the total number of pieces of candy by the number of friends: $48 \div 8 = 6$.
- ( a=1 ): ( b+c = 3 ). Nonnegative integer pairs: (0,3),(1,2),(2,1),(3,0) → 4 numbers.
- ( a=2 ): ( b+c=2 ) → (0,2),(1,1),(2,0) → 3 numbers.
- ( a=3 ): ( b+c=1 ) → (0,1),(1,0) → 2 numbers.
- ( a=4 ): ( b+c=0 ) → (0,0) → 1 number.
Total: ( 4+3+2+1 = 10 )
Solution Approach:
Most students start by factoring: ( n^2 + 9n + 14 = (n+2)(n+7) ). For this product to be prime, one factor must equal 1 (since a prime has exactly two positive divisors: 1 and itself).
The Sprint Round is the first and fastest-paced individual round of the competition. Art of Problem Solving 30 math problems to be solved in 40 minutes. Difficulty: