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SUBMIT YOUR IDEAI could not arrive at the same conclusion on the output; here is why.
I calculate there are (6*6*6) = 216 possible permutations; however, there are only 180 where Dice1 is greater than Dice2 or Dice 2 is greater than Dice 1, which is the same as Dice1 != Dice2. The mode of those 180 calculations is 7 and happens 12 times.
Where did I go wrong?
Fun stuff. I had a brain seizure along the way and found the expected value first.
My solution.