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anemone
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For any natural number $n$, let $S(n)$ denote the sum of the digits of $n$. Find the number of all 3-digit numbers $n$ such that $S(S(n))=2$.
The concept behind this problem is to find three-digit numbers where the sum of the squares of the digits equals 2. This means that when you square each digit and add them together, the result should be 2.
There are a total of 4 three-digit numbers that have a sum of digits squared equal to 2. These numbers are 109, 208, 307, and 406.
The easiest way to find these numbers is by using a systematic approach. Start by listing all three-digit numbers from 100 to 999. Then, calculate the sum of the squares of the digits for each number. If the result is 2, then that number is one of the solutions.
No, there is no specific formula for finding these numbers. However, you can use algebraic equations to represent the digits of a three-digit number and solve for the unknown digits.
This problem is a fun and challenging math puzzle that can help improve problem-solving skills and critical thinking. It also showcases the beauty and complexity of numbers and their relationships.