Before the question, just a short explanation of what a "digital root" is.
Assume that x is any set of numbers. If you add all the digits in all the numbers, then add the digits in the sum, and keep doing this until only one digit remains, that final digit is called the digital root of the original set x. One of the basic laws of digital roots is this. No matter how you scramble the digits of x to make a new set of numbers, the digital root of the new set will be the same as before. For example, consider the set of numbers 1, 23, and 931. The sum is 955. Adding the three digits gives 19, and 1 +9 = 10, and 1 +0 = 1, therefore the digital root of 1, 23, and 931 is 1. Now use the same digits to make a new set of numbers: 12, 13, and 39. The sum is 64. The digits add to 10, and 1 +0 = 1, therefore the digital root of 1, 23, and 931 has not altered.
My question is why does it happen? Is there a simple and informal explanation that can be explained to a high school student not much acquainted with formal mathematics?
Perhaps some intuitive explanation?
