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Here is the exercise from the "Arithmetic" book (ISBN: 5-02-013764-2).

There are 1989 numbers had printed to enumerate book's pages. How many pages in book?

Honestly I decided to refresh my arithmetic knowledge at all but stuck with that problem. Here's my decision:

  • there are 9 numbers to print for pages 1-9 (9 * 1);
  • there are 200 numbers to print for pages 10-99 (100 * 2);
  • 1989 - 209 = 1780;
  • 1780 /3 = 593,3(3) - that is the problem

I clearly understand how simple it must be and maybe something is wrong with my brain. But please, tell me where I made mistake.

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There are $90$ integers in the interval $[10,99],$ so your second line should be $90\times 2=180.$ – Andrew Aug 3 '12 at 18:32
Thanks a lot for correction. For me, I'm thinking about adult brain is less flexible than young and it thinks that he knows something and it's the must right thing. Sorry for such silly mistake. – Крайст Aug 3 '12 at 22:22
up vote 2 down vote accepted

There are not 100 numbers between 10 and 99. There are 10 between 10 and 19, 20 between 10 and 29, ..., 90 between 10 and 99. Each of those numbers has two digits. $2 \times 90 = 180$.

The rest of you're reasoning is perfectly sound. You just over-zealously counted the total number of two-digit numbers.

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oh… right! thank you very much. and i need a rest. – Крайст Aug 3 '12 at 22:16

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