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Fold blue 854 Posted 8 years ago
Grammar

Mathematics

There are 1000 people standing in a row. They are numbered as 1,2,...,1000. There is a unique demon who eats only the persons which are standing on odd positions. It means that after his first round the person numbered 2 will come at position 1 and the one at 4 will come at 2 and so on. So what is the assigned number of the person which is left at last ?
  

Top answer

Hi It's an interesting question because it leads into issues about infinite series. I could be wrong: there are 500 people with an odd number so, out of a thousand, we have 500 left. with an even number.

— Dave_anon

  • Hi It's an interesting question because it leads into issues about infinite series.
  • I could be wrong: there are 500 people with an odd number so, out of a thousand, we have 500 left.
  • with an even number.
  • Therefore, the last person in the list, after the demon, is the 500th Hope that's right!
  • Dave
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3 Answers
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Hi

It's an interesting question because it leads into issues about infinite series.

I could be wrong: there are 500 people with an odd number so, out of a thousand, we have 500 left. with an even number. Therefore, the last person in the list, after the demon, is the 500th

Hope that's right! Dave

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fold blue 854... what is the assigned number of the person which who is left at last ?

If you reassign numbers after each round, that last person to be eaten has to be the first and only person in line. So the assigned number is 1.

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But seriously, after the first round, you'll have this:

2 4 6 8 10 12 ... 996 998 1000

Every number is a multiple of 2 which is less than 1001.

Next you'll have:

4 8 12 ... 996 1000

Every number is a multiple of 4 which is less than 1001.

Next you'll have multiples of 8, then of 16, then of 32, and so on.

Eventually you'll be up to multiples

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