① Pages 1 to 9 : all single-digit numbers

Number of digits = 9 x 1 = 9


②Number of digits that go to the other pages

= 187 - 9
= 178

Pages 10 to 99 all contain double-digit numbers.

Number of pages from 10 to 99
= first 99 pages - first 9 pages
= 90

Or

99 - 10 + 1
= 89 + 1
= 90

(The number of numbers is always 1 more than the number of spaces/gaps between them)

Number of digits used for these 90 pages
= 90 x 2
= 180

③ Since we have only 178 digits that go to the other pages, the number of double-digit pages must be less than 90.

And this means there are no three-digit pages.

180 - 178 = 2

So we need to subtract 2 digits, or 1 page.

90 pages - 1 = 89 pages
So there are 89 two-digit pages.


Or

Number of two-digit pages
= 178 digits ÷ 2 digits per page
= 89

Total number of pages in the book

= 9(single digit) + 89(double-digit)
= 98

Check :

9 x 1 + 89 x 2

= 9 + 178
= 187

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