2021 WSMO Team Round Problems/Problem 2

Problem

Bobby has some pencils. When he tries to split them into 5 equal groups, he has 2 left over. When he tries to split them into groups of 8, he has 6 left over. What is the second smallest number of pencils that Bobby could have?

Proposed by pinkpig

Solution

We want $x \equiv 2 \pmod{5}$ and $x \equiv 6 \pmod{8}$ . The smallest such $x$ is $22$ , and the next is $62$ . So, our answer is $\boxed{62}.$ ~pinkpig

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2021 WSMO Team Round Problems/Problem 2

Problem

Solution