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Omni-MATH / How many subsets S of the set {1,2,…,10} satisfy the property that, for all i∈[1,9], either i or i+1 (or both) is in S?

Problem

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problem

How many subsets SS of the set {1,2,…,10}\{1,2, \ldots, 10\} satisfy the property that, for all i∈[1,9]i \in[1,9], either ii or i+1i+1 (or both) is in SS?
Plain-text mathematical notation (without MathML)
How many subsets S of the set {1,2,…,10} satisfy the property that, for all i∈[1,9], either i or i+1 (or both) is in S?
Original LaTeX notation
How many subsets $S$ of the set $\{1,2, \ldots, 10\}$ satisfy the property that, for all $i \in[1,9]$, either $i$ or $i+1$ (or both) is in $S$?

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Source and history

task_id
ffdf5fe5-b99a-5e02-96c9-340873ec8052
task_key
test--ffdf5fe5-b99a-5e02-96c9-340873ec8052
task_revision_id
1
config / split
/ test

Official source

initial import