50th Fastest And The 50th Slowest

Matt is the fiftieth fastest and the fiftieth slowest runner in his school.

Assuming no two runners are the same speed, how many runners are in Matt’s school?

Find here total number of runners! 

Total Runners In The School

Read the given data first!
 
This could be very tricky one. Let's assume that the Matt is fifth fastest and fifth slowest runner in his school.

Then there are 4 runners ahead of him numbered 1 to 4 and 4 behind him numbered 6 to 9. So there would be total 9 runners in his school in the case.

But Matt is 50th fastest runner meaning 49 are ahead of him numbered 1 to 49. And 49 are behind him numbered as 51 to 99 (total 49) while Matt is at 50th position.

Hence, there are 49 + 1 + 49 = 99 runners in his school.

A Rich Earl And Swamp

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."

Question 1: What did the earl think?

Question 2: And what do you think?

Go to the answers directly!

Planting Trees Covering Swamp

What's the exact story? 

The earl must have thought that planting 8 trees on first day itself would cause him to wait for only 10 days. That's totally wrong conclusion.

Though started with 8 trees, on other day number will be doubled only not tripled or increased to x8. Starting with 8 trees is like skipping 3 days (2,4,8) if started with 1 tree.That is only 3 days would be saved. 

In short, with 8 plants, the earl need to wait for 77 days!