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Never Decreasing Digits

Problem

A number has strictly increasing digits if each digit exceeds the digit to its left and is said to be a strictly increasing number; for example, 1357.
A number has increasing digits if each digit is not exceeded by the digit to its left and is said to be an increasing number; for example, 45579.

There are exactly 219 increasing numbers below one-thousand.

How many numbers below one million are increasing?

Problem ID: 263 (29 Jan 2006)     Difficulty: 4 Star

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