PuzzlersWorld.com

  • Hacker Puzzle
  • Interview Puzzles
  • Number Puzzles
  • Maths Puzzles

King and the Traveller Puzzle

(4 votes, average: 3.25 out of 5)

June 13, 2017 by Mohit Godara 1 Comment

A very intelligent and kind Traveller was trapped by a King, King wants to check his intelligence and kindness at the same time.

So he sets up a scenario where he asks traveller to play the “Sword Killing” game.

In this game ’N’ number of people have to stand in a circle in an order 1 to ’N’ and someone of them has a Sword, so when the game starts the person with the sword kills the left adjacent person and passes the sword to the next person, next person do the same again and this keeps on going until only one person survives at the end.
For example: – At starting, Person at 18th position have the sword, and the game starts, then the 18th position person kills 19th position person and passes sword to 20th position person, 20th person kills 21st person and passes sword to 22nd person and so on till only one person survives.

The twist King makes is that, he make the traveller stand at 489th position in the circle, and asks traveller to choose any number of people he wants to make stand in the circle, where traveller’s position will be fixed (489th) and also gave him option for starting this game from any position (Sword Initially with this position) . The basic rules for the game still remains same.

Given:
==>> SP (Starting Position): – Position of person the game starts from.
e.g. if SP=103 >> At starting Person at 103th position have the sword, and the game starts in a way that he kills 104 and passes it to 105 and so on till only one survives, which in this case should be 489th position person.
==>> N :- Total no. of people standing in the circle at the starting. N includes traveller as well.
For e.g. if N=500, it includes person standing at 489(or the traveller himself).
It is also understandable that N>=489
==>> Traveller is very Kind and wants to kill least no. of people as possible. Although he is kind but he prioritises his life over others.
i.e. he wants to save himself, but by killing minimum no. of people.

So you need to determine what would be value of N and SP, if Traveller wants to prove his kindness and intelligence.

Check your answer:
Value of N

Tried enough already?

Starting position

Tried enough already?
Answer With ExplanationHide
Will recommend to solve this puzzle before attempting to solve this one.

Answer: N = 489, SP = 223

Explanation:
We know that at the end only 1 person will survive, so he should handover the sword to a person such that he himself survives at the end. also to minimize the death’s N should be 489, as N can’t be smaller than 489 and if we add more persons, it means more people will die.

Now, it is important to notice that, if the number is a complete power of 2, the person who starts it survives.

Why? as lets assume we have 2^n persons, now after the round 1, half of the persons will be killed and the sword will be with the first person(who started) and now 2^(n-1) people will remain. and this will go one till 2^(1-1) = 2^0 = 1 person will remain(that will be the one who started it).

Now let’s find out the complete of 2 smaller than 489.

1,2,4,8,16,32,64,128,256,512

it is 256.

Now, if he ask someone to start such that when the sword comes to him, exactly 256 people should remain, he will survive at the end.

to do this, 489-256 = 233 people should die first.

thus if he asks 489 – 2*233 = 489 – 466 = 23rd person to start, when the sword will reach 489th person, 233 people will be dead with 256 people remaining. and we already proved that if total number of persons are a complete power of 2, person who starts survives.

  • Share on Whatsapp
  • Share on Facebook
  • Share on Twitter
Facebook Comments
Next Puzzle
Logic Puzzle: Pigeonhole Principle

Checkout more Logical Puzzles Tags: Difficult, Solved Puzzles

Comments

  1. vimal surana says

    June 13, 2017 at 3:12 pm

    N = 489 is perfect
    but sp is 23
    489-256 =233
    (233*2)+1= 467
    so the 467 person will not die
    so 489-467= 22
    so leaving this 22 person behind
    start from 23 person 489 will be 467th person

    Reply

Leave a Comment Cancel reply

Submit your Puzzle

You may also like

  • Hats and IIT students
  • Average salary
  • Confusing one!
  • Find Killer from calender clue
  • A lot of thought – parking number puzzle
  • Nine children in house
  • Philip says truth only one day
  • 4 letter words with atleast one vowel
  • if following relationship holds then what is value of 9
  • Did i speak to Tina or Meena ?

Categories

  • Aive hi Puzzles
  • Akbar and Birbal
  • Alphabetical Puzzles
  • Bollywood Puzzles
  • Google Code jam
  • Hindi Riddles
  • Interview Puzzles
  • Interview Questions
  • Logical Puzzles
  • Malayalam Puzzles
  • Maths Puzzles
  • Miscellaneous
  • Number Puzzles
  • Picture Puzzles
  • Riddles
  • Tamil Puzzles
  • Technical

Social

  • View puzzlersworld’s profile on Twitter
privacy policy

Copyright © 2025 · eleven40 Pro Theme on Genesis Framework · WordPress · Log in

  • Hacker Puzzle
  • Logo Puzzles
  • Optical Illusions
  • WhatsApp Puzzles
  • Picture Puzzles
  • Riddles
    ▼
    • Hindi Riddles
  • Bollywood Puzzles
  • Alphabetical Puzzles
  • Aive hi Puzzles
  • Interview Puzzles
  • Logical Puzzles
  • Interview Questions
    ▼
    • Data Structures
    • Binary Tree
    • Algorithms
    • Recursion Questions
    • Amazon Interview Questions
    • Snapdeal Interview Questions
    • Google Code jam
  • Technical
  • Akbar and Birbal
  • Number Puzzles
  • Maths Puzzles
  • Miscellaneous