Smallest array forcing 7 probes

Binary search on a sorted array of nn elements needs ⌈log⁡2(n+1)⌉\lceil \log_2(n+1) \rceil comparisons in the worst case. What is the smallest array size nn for which the worst case reaches exactly 7 comparisons?

Show hints (2)+
  1. ⌈log⁡2(n+1)⌉=7\lceil\log_2(n+1)\rceil = 7 means 6<log⁡2(n+1)≤76 < \log_2(n+1) \le 7.
  2. Exponentiate: 64<n+1≤12864 < n+1 \le 128, so the smallest nn is at the low end.

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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