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King and the Traveller Puzzle

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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?

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Four wise men with hats puzzle

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Four wise men are wearing Black and White hats so that each of them can only see the others’ hats.

They are told that at least one of their hats is white and at least one is black.

Asked, in turn, if they can tell the color of their own hat?

The first wise man says no, then the second wise man says no, but then the third wise man could give the right answer.

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Bar with 25 seats

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There is a bar with 25 seats in a line. The people there are anti-social so when they walk in the bar, they always try to find a seat farthest away from others. If one person walks in and find there is no seat are adjacent to nobody, that person will walk away. The bar owner wants as many people as possible. The owner can tell the first customer where to sit. all the other customers will pick the farthest possible seat from others.
So where should the first customer sit?
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