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Blue 2 = 2
2 squared = 4
-2 yellow = 2
+ 2 blue = 4
4 Squared = 16
2x2 = 4
4-2 = 4
2+2 = 4
4 squared is 16.
You're not squaring the number that's on the board, you're squaring the total *after* completing that operation.
You need to check your third line. You have written 4-2 = 4.
A bit of further clarification: you don't square the result after each operation, but you square the result after each ring using that operation.
Say you got 3 blue numbers in the second ring with a blue square on the bullseye, you then add all three of them to the result of the first ring and only then square the result of that.
Also, it's kind of crazy to assume the puzzle is broken after you've played a modest amount of the game, rather than question if the rules are not what you believe them to be.
"...that I was definitely solving correctly".
You did say that "The Answer is DEFINITELY either 4 or 6." when you still had misunderstandings about how the puzzle worked. I don't know if the place you looked up gave you wrong information or if you misunderstood it.
The puzzle is clearly explained *in other places*, which was what Vercci was trying to explain. Not every explanation is given NEXT to the puzzle.