Answers to 11-hour clock questions

To find the standard name of a positive number, alternately subtract and add the digits, starting with the ones digit and working to the left. If the result is more than 10, repeat until you get a number small enough.
Example: 192807 = 7 - 0 + 8 - 2 + 9 - 1 = 21 = 1 - 2 = -1 = 10 (mod 11). For negative numbers, do the same to get a negative number, then add 9.
Example: -37 = -(7 - 3) = -4 = -4 + 11 = 7 (mod 19).

This is a well-known divisibility test for factors of 11, but it also gives the remainder for division by 11 if used carefully.

Answers to addition and subtraction questions.

  1. 1
  2. 1
  3. 0
  4. 0
  5. 10
  6. 7
  7. 4
  8. 3
  9. 10
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