Mathcounts National Sprint Round Problems And Solutions |work|

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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

Let’s re-read: “positive integers (n)” and “is a prime number.” If (n=1): (3)(8)=24, not prime. n=2: (4)(9)=36. n=3: (5)(10)=50. n=4: (6)(11)=66. n=5: (7)(12)=84. It seems never prime. Let’s re-read: “positive integers (n)” and “is a

Solution Path:To find the probability of "at least two red," we sum the cases for exactly 2 red and exactly 3 red. n=4: (6)(11)=66

Problems 21 through 30 escalate rapidly in complexity, often reaching the difficulty level of the Team Round .