When Multiples And Digit Sums Collide

Number Theory Level 1

How many positive integers \(n\) from 1 to 1000 (inclusive) are there, such that \(n\) is a multiple of 3, and the digit sum of \(n\) is also a multiple of 3?

Details and assumptions

The digit sum of a number is the sum of all its digits. For example, the digit sum of 1123 is \(1 + 1 + 2 + 3 = 7\).

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.