Question

50 people are standing in a circle in an order 1 to 50, No. 1 has a sword. He
kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3).
All people do the same until only 1 survives. Which number survives at the
last?

Answer 1

Answer:

37 number will survive.

Answer 2

Concept:

The study of natural numbers and integers is the focus of the pure mathematics discipline known as number theory. It is the study of the collection of complete positive numbers, sometimes known as the natural number collection. Number theory is also referred to as "The Queen of Mathematics" due to the fact that it serves as the discipline's cornerstone.

GIVEN:

50 people are standing in a circle in an order 1 to 50, No. 1 has a sword. He

kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3).

All people do the same until only 1 survives.

Find:

Which number will survive?

Solution:

Let all no. be in a row for simplicity

1,2,3,............................50

2n no.s are killed, 2n+1 will survive

1,3,5..........................49

4n+3 no.s are killed, 4n+1 will survive

5,9...............49

8n+1 will survive

9,17,25,33,41,49

16n+1 will survive

17,33,49

32n+1 will survive

33 will survive

Therefore, only 33 will survive

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