Repeating Digits in Addition

  1. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = ?
  2. 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = ?
  3. 111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999 = ?
  4. What is going on here? Does this pattern work for 4-digit addends, 5-digit addends, and so on?


Show/Hide Solution

  1. 45
  2. 495
  3. 4995
  4. The first digit is 4; the last is 5. The rest of the digits are 9’s and there is one less 9 than the number of digits in the numbers being added. This pattern also works for 4- and 5-digit addends. Um, why?

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