Problem 22 · 2020 Math Kangaroo
Stretch
Counting & Probability
divisibilitylast-digit
Julia puts the nine chips shown into a box. She then takes one chip at a time, without looking, and notes down its digit, obtaining at the end a number with nine different digits. What is the probability that the number written by Julia is divisible by 45?
Show answer
Answer: A — 19
Show hints
Hint 1 of 2
Divisible by 45 means divisible by both 9 and 5.
Still stuck? Show hint 2 →
Hint 2 of 2
The digits 1–9 always sum to 45, so 9 is automatic — only the last digit matters for 5.
Show solution
Approach: reduce to a single last-digit condition
- 1+2+…+9 = 45, so any arrangement is divisible by 9.
- Divisibility by 5 needs the last digit to be 5 (there’s no 0).
- The chance the last chip drawn is 5 is 1/9.
- So the probability is 1/9.
Mark:
· log in to save