Multiple choice general knowledge math & puzzles

A rich earl has become the owner of a piece of land, which to his dissatisfaction turned out to be nothing more than a big swamp. The earl wants to get rid of the swamp. A salesman advises him to use his fast-growing plants which can cover the swamp very quickly. "This plant doubles every day, tomorrow you will have two, the day after tomorrow four, etc. In 80 days, your swamp will be completely covered." The earl reacts: "80 days? This takes far too much time. Then just give me eight of these plants." How Many days will Earl Save by taking 8 plants ??

  1. 3

  2. 67

  3. 70

  4. 77
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

With 1 plant, the swamp is covered in 80 days (2^80 plants needed). With 8 plants, you start with 8 = 2^3 plants. So you need 2^77 more plants, which takes 77 days. By starting with 8 plants, the earl saves 80 - 77 = 3 days. Each plant doubles daily, so having 8 plants is equivalent to being 3 days ahead (since 2^3 = 8).

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