Problem 7 · Start from the extreme · 5 points
Made by AI and not reviewed by a real person.
A three-digit number has digits that add up to 26. How many such numbers are there?
- 3
- 1
- 5
- 4
- 2
Show a hint
- What is the biggest digit sum a 3-digit number can have?
- You need a sum only 1 less than the maximum.
Show the answer and solution
Answer: A — 3
The maximum digit sum is 9 + 9 + 9 = 27, so a sum of 26 means the digits are 9, 9, 8 in some order: 998, 989, 899 — three numbers. Anchoring at the extreme case and stepping back from it shrinks a huge search to almost nothing.