Question: What is the remainder when $ 123456789 $ is divided by 9?
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- Solution: The 100th signal occurs at minute:
- \times (100 - 1) = 13 \times 99 = 1287
- So the minute number of the 100th signal is $ \boxed{1287} $.
- Solution: Use the divisibility rule for 9: the remainder when a number is divided by 9 is the same as the remainder when the sum of its digits is divided by 9.
- Sum of digits of 123456789:
- + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
