The citizens of planet nigiet are 8 fingered and have thus developed their…
2024
The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
- A.
192
- B.
100
- C.
150
- D.
145
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Correct answer: A
Answer: 192
Reasoning:
Buildings numbered 1 to 1000 in base 8 cover all octal numbers from 000 to 777 (512 numbers) and include 1000 (base 8) which has no digit 3, so counting 000–777 suffices.
Across these 512 numbers each digit position (units, eights, sixty-fours) cycles evenly through 0–7, so digit 3 appears 512 ÷ 8 = 64 times in each position.
Total occurrences of digit 3 = 3 positions × 64 = 192.
Therefore, the digit 3 is used 192 times in numbering the buildings.