A book's pages are numbered starting from 1. If the printer used 3189 individual digits to print all page numbers, how many pages does the book contain?

Introduction / Context:
This is a classic digit-counting problem on page numbers. We calculate how many digits are needed to print page numbers 1 to N and match the total 3189 to find N. Such questions strengthen place-value reasoning and arithmetic series logic.

Given Data / Assumptions:

• Pages start at 1 and go consecutively up to N.
• Total digits used to print all page numbers = 3189.
• We count digits by ranges of lengths: 1-digit, 2-digit, 3-digit, etc.

Concept / Approach:
Break page numbers into intervals with constant digit lengths, then sum: 1–9 (9 pages, 1 digit each), 10–99 (90 pages, 2 digits each), 100–999 (900 pages, 3 digits each), and so on. Accumulate digits until we reach or exceed 3189, then solve for the remainder in the last interval.

Step-by-Step Solution:
Digits for 1–9: 9 * 1 = 9.Digits for 10–99: 90 * 2 = 180. Cumulative = 9 + 180 = 189.Remaining to reach 3189: 3189 - 189 = 3000 digits.Now use 3-digit pages from 100 upward: each page consumes 3 digits.Number of 3-digit pages required = 3000 / 3 = 1000 pages.Thus pages run from 100 to 1099 inclusive (1000 pages). Final page N = 1099.But verify cumulative: 1–99 used 189 digits; 100–1099 uses 1000 * 3 = 3000 digits; total = 3189 digits. Hence N = 1099. Wait—this contradicts options; reconcile carefully.Recheck: 100–999 is 900 pages * 3 = 2700 digits. Add to 189 → 2889. Remaining = 3189 - 2889 = 300 digits. These 300 digits belong to pages from 1000 onward (4-digit numbers, 4 digits each).Pages with 4 digits used = 300 / 4 = 75 pages.Therefore last page = 999 + 75 = 1074.

Verification / Alternative check:
Compute exact totals: 1–9 → 9; 10–99 → 180; 100–999 → 2700; subtotal = 2889; add 1000–1074 → 75 * 4 = 300; total = 3189. Matches perfectly.

Why Other Options Are Wrong:

• 1000: Would require only 2889 + 1 * 4 = 2893 digits, far short of 3189.
• 1075: Would use 304 digits beyond 999, totaling 3193 digits, too many.
• 1080 and 1150: Exceed 3189 digits when computed precisely.

Common Pitfalls:

• Jumping directly from 3-digit to a large 4-digit span without careful subtraction.
• Arithmetic slips in subtracting 2889 from 3189.

Final Answer:
1074