Problem 2 · 2022 Math Kangaroo
Medium
Number Theory
careful-counting
Karo has a box of matches with 30 matches. Using some of the matches she forms the number 2022. She has already formed the first two digits (see picture). How many matches will be left in the box when she has finished the number?
Show answer
Answer: B — 9
Show hints
Hint 1 of 2
Work out how many matches each digit needs, then add up what is still missing.
Still stuck? Show hint 2 →
Hint 2 of 2
She has already built '20'; only '22' remains, and each '2' costs 5 matches.
Show solution
Approach: count matches used, subtract from 30
- A '2' is built from 5 matches and a '0' from 6 matches.
- Forming '20' already used 5 + 6 = 11 matches.
- The remaining digits '22' need 5 + 5 = 10 matches.
- Matches left = 30 - 11 - 10 = 9.
Mark:
· log in to save