Tricky Puzzle

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You’re escaping a labyrinth, and there are three doors in front of you. The door on the left leads to a raging inferno. The door in the center leads to a deadly assassin. The door on the right leads to a lion that hasn’t eaten in three months.
Which door do you choose?
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A person was prescribed to take two pills (tablets), one each, from the two bottles viz. Bottle A and Bottle B, daily. The tablets are exactly look alike.
The medicines have to be taken exactly one tablet from each bottle, neither less nor more, else the medicines will not be effective.
One fine day, the patient popped out one tablet from Bottle A, but while taking the tablet from bottle B, by mistake, two tablets spilled over. Now he has three tablets in his hand, and he can’t put back the extra tablet to Bottle B as all the tablets are identical in looks.
He has to ensure that he takes exactly one tablet from each of the bottles and at the same time he must avoid any wastage of the medicine. What He will do?
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371 is a number that can be expressed as the sum of cube of its digits,
i.e., 371=3^3 + 7^3 + 1^3
Can you name another such 3digit number within a minute?
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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.
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A woman goes to the counter and puts a book before the man there. The man says that the price is 13. The lady pays the money and goes away without taking the book. The man saw it and did not call the lady.
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Given six distinct colors, in how many unique ways can a sixfaced cube be painted such that no two faces have the same color?
Note: The mixing of colors is not allowed.
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