I agree there is a problem with the overrule, a small problem, the big problem is what you call definitive knowledge...at best you had definitive knowledge of putting 3.6 seconds on the clock. I agree that most likely it would have run out, but most likely is non definitive knowledge. The book mentions what can be used and you were correct that you can use your count...but you can't guess at the rest all you can do is make it as correct as possible...by the book anyway...I probably would have gone with 3 seconds on the clock in my game...then again it is a lower level game so a good time to learn...
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