Mathcounts National Sprint Round Problems And Solutions (2025)

( \boxed10 )

The zero-digit trick: if any digit is 0, product is automatically a multiple of 8. That simplifies counting drastically. Mathcounts National Sprint Round Problems And Solutions

How many positive integers less than 100 are divisible by 3 or 5 but not by both? ( \boxed10 ) The zero-digit trick: if any

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. since MATHCOUNTS is free-response