Let’s examine five representative problems drawn from past National Sprint Rounds, ranging from medium to extremely difficult.

A certain number is doubled and the resulting number is decreased by 3 to get 99. What is the original number? Let the original number be Follow the operations: Add 3 to both sides: Divide by 2: Problem 2: Rate and Distance

This problem asked for the total length of a graph defined by an equation involving square terms and absolute values.

“Distinct” vs. “not necessarily distinct,” “positive integers” vs. “nonnegative,” “inclusive” vs. “exclusive.”

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

The AoPS Wiki is the most extensive community-driven resource, featuring an archive of problems and solutions for past National Sprint Rounds.