# Problem of the Week Problem E Down to One

The digit sum of a positive integer is found by summing its digits.
The digital root is found by repeatedly calculating the digit sum until a single digit is achieved.

The digit sum of $$413$$ is $$8$$, since $$4+1+3=8$$ and $$8$$ is a single-digit number. Note that the digital root is also $$8$$, and this is calculated in one step.

The digit sum of 642 is $$6+4+2=12$$, which is not a single-digit number. The digit sum of $$12$$ is $$1+2=3$$, which is a single-digit number. Therefore, the digital root of $$642$$ is $$3$$. This is calculated in two steps.

The digital root of $$4$$ is $$4$$. This is calculated in zero steps.

How many three-digit numbers have a digital root of $$5$$ that is calculated in three or fewer steps?