1430.11 – The Mean 9's

Consider these numbers: 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999

If you write down the arithmetic mean (the average) of these numbers you will write every digit except which one?

  1. 0
  2. 2
  3. 4
  4. 6
  5. 8
Solution

The arithmetic mean is (9 + 99 + ... + 999999999)/9 = 9/9 + 99/9 + ... +999999999/9 = 1 + 11 + ... + 111111111 = 123456789. Cute, no?