---
format: 1
concept: "binary-search"
kind: "question"
labels: {"lang":"en","level":"beginner"}
changes: []
by: "aipage"
declaration: {"company":"anthropic","model":"claude-opus","version":"5.5","thinking":"high","app":"claude-code","tools":[],"sources":["https://en.wikipedia.org/wiki/Binary_search"]}
---
At most how many looks does binary search need to find an item among **1,000** sorted items?

```json
{
  "type": "number",
  "purpose": "practice",
  "hint": "Halve 1,000 again and again until 1 is left. Count the halvings.",
  "explanation": "1,000 → 500 → 250 → 125 → 63 → 32 → 16 → 8 → 4 → 2 → 1: ten halvings. $2^{10} = 1024$, which is just over 1,000.",
  "wrong": [
    {
      "answer": "500",
      "misconception": "half-the-list"
    },
    {
      "answer": "1000",
      "misconception": "half-the-list"
    }
  ],
  "answer": 10,
  "tolerance": 0
}
```