Problem 8 · 2019 Math Kangaroo
Medium
Number Theory
careful-countingplace-value
Julia reads a book whose pages are all numbered. The digit 0 appears five times and the digit 8 appears six times. What is the page number of the last page?
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Answer: B — 58
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Hint 1 of 2
Count how many 0s and 8s appear as you number pages 1, 2, 3, and so on.
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Hint 2 of 2
Stop at the page where the 0-count and 8-count first match the clue.
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Approach: tally the digits up to each candidate
- Counting digits from page 1: the digit 0 first reaches five copies and the digit 8 first reaches six copies at the same point.
- Tallying shows that happens exactly at page 58 (zeros in 10,20,30,40,50; eights in 8,18,28,38,48,58).
- So the last page is 58.
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