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Museion Original · Computer Science

extension · Ages 14+ · basic arrays

Search by Halving

Build binary search from its invariant, not from copied code.

Start the path 3 lessons · about 55 minutes
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Three connected investigations

  1. 01Prepare a Search SpaceFor learners ages 14+ who can read arrays: decide when halving is valid, predict the useful side, and set inclusive boundaries.Open
  2. 02Keep the Target in the IntervalFor learners ages 14+ who understand sorted arrays and zero-based indices: trace inclusive binary search without losing a possible target.Open
  3. 03Reason About Repeated HalvingFor learners ages 14+ who can trace binary search: count candidate reductions, compare growth carefully, and transfer the invariant to a new sorted search.Open

What this path asks you to reason about

  • Audit whether binary-search discard rules are valid for an input.
  • Trace inclusive low, high, and midpoint updates without off-by-one loss.
  • Explain logarithmic comparison growth without inventing timing evidence.