Solution:

Let's consider a number and its reverse to see how the digit sum changes.

1. Example 1: A 2-digit number

   • Let the number be 47.
   • Its digits are 4 and 7.
   • The digit sum of 47 is $4+7=11$.
   • When 47 is reversed, the new number is 74.
   • Its digits are 7 and 4.
   • The digit sum of 74 is $7+4=11$.

2. Example 2: A 3-digit number

   • Let the number be 123.
   • Its digits are 1, 2, and 3.
   • The digit sum of 123 is $1+2+3=6$.
   • When 123 is reversed, the new number is 321.
   • Its digits are 3, 2, and 1.
   • The digit sum of 321 is $3+2+1=6$.

3. General Explanation:

   The digit sum of a number is the sum of its individual digits. When a number is reversed, the order of its digits changes, but the set of digits themselves remains exactly the same. For example, if a number is $d_n{d}_{n-1}\dots d_1{d}_0$, its digit sum is $d_n+d_{n-1}+\dots +d_1+d_0$. When reversed, the number becomes $d_0{d}_1\dots d_{n-1}{d}_n$, and its digit sum is $d_0+d_1+\dots +d_{n-1}+d_n$. Due to the commutative property of addition, the sum remains the same regardless of the order of the digits.

Final Answer: The digit sum of a number does not change when the number is reversed. This is because the operation of summing digits is commutative, meaning the order in which the digits are added does not affect the total sum. For example, the digit sum of 47 is $4+7=11$, and the digit sum of its reverse, 74, is also $7+4=11$.