The "Series" Series - Problem 3

Algebra Level 5

A positive integer will be called awesome if it has the following properties:

  1. It ranges between \(10000\) and \(100000\), not inclusive. Therefore an awesome integer must contain \(5\) digits.

  2. The ten thousands digit is less than the thousands digit.

  3. The thousands digit is less than the hundreds digit.

  4. The hundreds digit is less than the tens digit.

  5. The tens digit is less than the ones digit.

Robert writes ALL possible awesome integers on a piece of paper. He then arranges them in ascending order, putting them in a sequence \(a_{n}\) in which \(a_{1}\) has the smallest value, and \(a_{n}\) has the biggest value. Find \(n + a_{100}\)

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