[zdance]

37 is irreducible in the problem statement, so the answer is 37.

Think about it purely in the set-theoretic sense "what is the minimal set containing 37 elements?" the answer is "the set containing 37 elements."

[Dylan16807]

The fixed 37 is the value of the coins. It's very easy to reduce the number of coins.

Either you misunderstood something or please explain more. Note that both the working and broken versions have the same 37 in them.

And the problem statement starts with no coins chosen. It had to actively choose pennies to get that broken result. If you told it about the coins in a different order, it probably would have given a different answer.