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added 72 characters in body
Kevin Cruijssen
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#05AB1E, 16 14 13 bytes

ćs3L×0KJ‚€{íË

Input order is [reputation, bronze_medals, silver_medals, gold_medals].

Try it online or verify all test cases.

Explanation:

ć              # Extract the head of the (implicit) input-list;
               # pop the list and push the remainder-list and head separately to the stack
 s             # Swap to get the remainder-list at the top again
  3L           # Push the list [3,2,1]
    ×          # Repeat the remainder-numbers that many times as string
     0K        # Remove all 0s (so all "0", "00" and "000")
       J       # Join the strings in the list together
        ‚      # Pair this string with the head
         €{í   # Sort the digits in both strings in descending order
            Ë  # And check if both are now equal
               # (after which the result is output implicitly as result)
Kevin Cruijssen
  • 131.4k
  • 13
  • 144
  • 384