(Solution) - Let n 2k for k Z We use -(2025 Original AI-Free Solution)

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Let n = 2k for k ? Z+. We use the n k-bit sequences (of 0's and l's) to represent 1, 2, 3, . . . , n, so that for two consecutive integers i, i + 1, the corresponding k-bit sequences differ in exactly one component. This representation is called a Gray code (comparable to what we saw in Example 3.9).
(a) For k = 3, use a graph model with V = {000, 001, 010, . .. , 111} to find such a code for 1, 2, 3, . . . , 8. How is this related to the concept of a Hamilton path?
(b) Answer part (a) for k = 4.