Problem 10 · 2019 Math Kangaroo
Medium
Number Theory
digit-sumcareful-counting
Julia reads a book whose pages are all numbered. The digit 0 appears six times and the digit 8 seven times. What is the page number of the last page?
Show answer
Answer: B — 68
Show hints
Hint 1 of 2
Count how many 0s and 8s appear as you number pages 1, 2, 3, …
Still stuck? Show hint 2 →
Hint 2 of 2
Zeros first appear at 10, 20, … and eights at 8, 18, 28, … — find where the counts hit 6 and 7.
Show solution
Approach: tally occurrences of 0 and 8 up to the last page
- Zeros appear at 10, 20, 30, 40, 50, 60 — the sixth zero is on page 60.
- Eights appear at 8, 18, 28, 38, 48, 58, 68 — the seventh eight is on page 68.
- Both counts are first met by page 68.
Mark:
· log in to save