The root of all digits

Number Theory Level 3

The digital root (also repeated digital sum) of a non-negative integer is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.

For example, the digital root of \(487\) is \(1\):




What is the digital root of \(123,456,\ldots,497,498,499,500\)?

Note: The number above is a base 10 number in which the digits are formed from consecutive integers from 1 to 500.


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