For N=4N = 4N=4: 4×1/8=1/24 \times 1/8 = 1/24×1/8=1/2. That matches our simulation. But we can only add probabilities when the events are mutually exclusive (no two can happen at the same time). Can two of these events overlap?
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Writing specifications is not always easy, but it is easier than writing the optimized implementation. And a powerful shortcut exists: an inefficient program that is obviously correct can serve as its own specification. User and AI co-write a simple model, AI writes an efficient version, and proves the two equivalent. The hard part shifts from implementation to design. That is the right kind of hard.
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