Problem 1 · Build greedily, digit by digit · 3 points
Made by AI and not reviewed by a real person.
What is the smallest 3-digit number in which all three digits are different?
- 123
- 120
- 102
- 100
- 101
Show a hint
- Make the hundreds digit as small as allowed, then the tens digit, then the ones.
Show the answer and solution
Answer: C — 102
Hundreds digit: smallest allowed is 1 (0 would not give a 3-digit number). Tens: smallest unused is 0. Ones: smallest still unused is 2. Answer: 102. (100 repeats 0, 101 repeats 1.) Choosing the best option position-by-position is called a greedy strategy — and knowing when it works is real mathematical judgment.