Armstrong Number

A number is an Armstrong number (narcissistic number) if it equals the sum of its own digits each raised to the power of the number of digits. For example, $153 = 1^3 + 5^3 + 3^3$. Write a function that returns True if a number is an Armstrong number.

For a number with $d = \lfloor \log_{10} N \rfloor + 1$ digits, it is Armstrong if $N = \sum_{i} d_i^d$ where $d_i$ are its digits. The key insight is that you need the total digit count before summing — compute it once, then extract each digit using the modulo loop from Day 1.

1. Count the number of digits: d = len(str(n)) or using $\lfloor \log_{10} N \rfloor + 1$.
2. Extract digits one by one using n % 10 and n // 10.
3. For each digit, raise it to the power d and add to a running sum.
4. Compare the sum to the original number.

• Computing the number of digits inside the loop (recalculated wrongly as digits are removed)
• Using n % 10 after modifying n without saving the original — always save original = n
• Only testing single-digit numbers (1–9 are trivially Armstrong); test 153, 370, 371, 407

Armstrong numbers combine two patterns you've already seen: digit extraction (Day 1, Day 2) and exponentiation. The important lesson here is to compute num_digits once before the loop, not inside it.