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They do indeed have an internal relation - they all add up to 2025.

Obviously all the formula will be equivalent to each other. They are, by construction, all restatements of each other.

I guess that means that every number is equivalent to a formula? Is there some sort of metric of how many formula produce the same number?

You’d have to at least exclude subtraction and division (and zero) to not have infinitely many formulas for every number.

I would say that a rule is "cheating" iff it is implied by another rule for any arbitrary N.