I Found Hidden Solutions to a Viral Math Puzzle — Here's How

A video went viral recently showing a neat math trick: Take a number, find its nth root, and check if that equals the digit sum minus n. The original showed just 4 examples: Expression Digit Sum − n Result √25 = 5 (2+5) − 2 = 5 ✅ √64 = 8 (6+4) − 2 = 8 ✅ ³√125 = 5 (1+2+5) − 3 = 5 ✅ ³√4096 = 16 (4+0+9+6) − 3 = 16 ✅ Cool party trick. But as a developer, my first thought was: are there more? Brute-Forcing the Answer I wrote a simple script to check every combination: def digit_sum ( n ): return sum ( int ( d ) for d in str ( n )) solutions = [] for n in range ( 2 , 20 ): # root degree (2=square, 3=cube...) for number in range ( 1 , 1_000_000 ): # check up to 1 million root = round ( number ** ( 1 / n )) # Verify it is a perfect nth root if root ** n != number : continue # Check the pattern: nth_root == digit_sum - n if root == digit_sum ( number ) - n : solutions . append (( n , number , root )) print ( f " { n } root( { number } ) = { root } " f " (digit sum { digit_sum ( number ) } - { n