Available Hints:
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The card with the ?'s shows how to find the four solution numbers in order. The other cards are clues to how the system works.
Each of the six animals has a consistent behavior you can identify.
Each path starts with a number. The animals' behaviors are mathematical, and they are applied in sequence following the arrows.
The hedgehog and the shark are the easiest to figure out. Try to get them first.
The butterfly and the monkey are the next easiest to figure out after the hedgehog and shark. The monkey's behavior is more complex than the first three. Don't worry, I only used integers.
The lizard and the scorpion are the hardest to figure out. Do them last. The lizard is the weirdest of all.
The hedgehog and shark are simple addition and subtraction. The butterfly and scorpion are multiplication. The monkey is a square root.
The lizard produces 10 minus what he is given. So, 1 -> Lizard = 9, 5 -> Lizard = 5.
The hedgehog is +5, the shark is -3, the butterfly is x2, and the scorpion is x (-1). That means the first equation calculates to 5, as follows: 0x2 = 0, square root 0 = 0, 0 x (-1) = 0, then five hedgehogs (+5 each) make it 25, and another monkey square root gets you to 5. The others solve to 2, 7, and 9.