A group of gnomes have once again somehow become victims to the whims of a particularly virulent puzzle-loving wizard. The wizard has a new puzzle in mind and he's curious to see whether his gnomes can outwit him. He tells the gnomes of his plan:
"I'm going to shackle every one of you little rats to a chain and place you single-file in a line. You must all face forward - no looking about! Anybody looks about and you all get fried. Each of you shall wear a hat of a color of my choosing. Since you are a rediculously stupid little pack of runts, we'd better keep it simple: hats will be black or white. Starting in the back I will then walk down the line and ask each of you a very simple question: What is the color of your hat? You may then answer Black or White. Anybody answers otherwise and you all get toasted! If the answer is correct, that gnome's life will most generously be spared. Answer incorrectly, and I will feed you to my pet naga, so you'd better give your answer some thought! You may now take some time to formulate a plan, lest you all be fed to the beast! There is, however, one condition: you must fully inform me of your strategy. Anyone deviates from the strategy, and you all become naga lunch!"
It looks like the gnomes are knee-high in trouble. Can you formulate a strategy to save the highest number of gnomes? Keep in mind that, since the wizard knows your strategy, he will be working against you to ensure that the maximum number of gnomes will be fed to his beloved naga.
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