Absolutely lazy mistake

Algebra Level 3

Jook believes that since Math is beautiful, it must always work out. This leads him to think that

\[ | a-c | = | a - b | + | b - c |, \]

with the reasoning that "\(-b\) and \(+b\) will cancel out". How many ordered sets of integers \( (a, b, c) \), each of which are between 0 and 10 (inclusive), satisfy

\[ | a-c | = | a - b | + | b - c |? \]

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, interactive explorations.

Used and loved by over 5 million people

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