There room 100 doors. 100 strangers have been gathered in the adjacent room. The first one goes and opens every door. The second one goes and also shuts down all the also numbered doors – second, fourth, sixth... And so on. The third one goes and also reverses the present position of every 3rd door (third, sixth, ninth… and also so on.) i.e. If the door is open, he turn off it and if the door is shut, the switches opens up it. All the 100 strangers progresses in the similar fashion. After ~ the critical person has done what that wanted, i beg your pardon doors will be left open and also which ones will be shut at the end?
Solution:

Think deeply around the door number 56, world will visit it because that every divisor the has. Therefore 56 has 1 & 56, 2 & 28, 4 & 14, 7 & 8. For this reason on happen 1, the 1st person will open the door; happen 2, 2nd one will certainly close it; happen 4, open; happen 7, close; pass 8, open; pass 14, close; happen 28, open; pass 56, close. Thus we deserve to say that the door will certainly just finish up earlier in its original state because that each pair that divisor. However what about the cases in which the pair the divisor has actually analogous number for example door number 16? 16 has the divisors 1 & 16, 2 & 8, 4&4. But 4 is recurrent because 16 is a perfect square, so girlfriend will just visit door number 16, on pass 1, 2, 4, 8 and also 16… leaving it open at the end. So just perfect square doors will remain open at the end.

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Mind Teasers :Interview Marble logic Puzzle

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You are given a collection of scales and also 12 marbles. The scales space of the old balance variety. That is, a small dish hangs indigenous each finish of a rod that is well balanced in the middle. The device enables you come conclude either that the components of the dishes sweet the very same or the the dish that drops lower has actually heavier materials than the other.The 12 marbles appear to be identical. In fact, 11 that them space identical, and also one is the a different weight. Your job is to determine the inexplicable marble and discard it. You are permitted to usage the scales 3 times if you wish, however no more.Note that the unexplained marble might be heavier or lighter 보다 the others. You room asked come both recognize it and determine whether it is heavy or light.
Solution:

So that the following setup can be followed, let united state number the coins native 1 come 12. For the an initial weighing permit us placed on the left pan coins 1,2,3,4 and also on the ideal pan coins 5,6,7,8.There room two possibilities. Either they balance, or they don"t. If lock balance, climate the various coin is in the group 9,10,11,12. So because that our second one opportunity is to weigh 9,10,11 against 1,2,3(1) lock balance, in which situation you understand 12 is the different coin, and you simply weigh it against any various other to identify whether it is heavy or light.(2) 9,10,11 is heavy. In this case, you recognize that the various coin is 9, 10, or 11, and also that that coin is heavy. Just weigh 9 against 10; if lock balance, 11 is the heavy coin. If not, the more heavier one is the hefty coin.(3) 9,10,11 is light. Continue as in the step above, but the coin you"re searching for is the irradiate one.That was the straightforward part.What if the very first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then any one of these coins could be the different coin. Now, in order come proceed, we have to keep track of which next is heavy for every of the following weighings.Suppose that 5,6,7,8 is the heavy side. We currently weigh 1,5,6 versus 2,7,8. If lock balance, then the various coin is one of two people 3 or 4. Weigh 4 against 9, a known an excellent coin. If they balance then the various coin is 3, otherwise it is 4. The direction the the tilts can tell us whwther the offending coin is heavier or lighter.Now, if 1,5,6 vs 2,7,8 does no balance, and also 2,7,8 is the hefty side, then either 7 or 8 is a different, hefty coin, or 1 is a different, irradiate coin.For the 3rd weighing, weigh 7 against 8. Whichever side is heavy is the various coin. If lock balance, climate 1 is the different coin. Must the weighing that 1,5, 6 vs 2,7,8 show 1,5,6 to it is in the hefty side, climate either 5 or 6 is a different heavy coin or 2 is a light different coin. Weigh 5 against 6. The more heavier one is the various coin. If castle balance, then 2 is a various light coin.

Mind Teasers :Candle trick Teaser Problem

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Husband has prepared for a candle irradiate dinner on the honeymoon because that his wife. While they were having the dinner, a solid breeze flew v the open window and 4 candles the end of ten to be extinguished. After ~ that, the husband closed the window. How many candles to be left in the end?
Solution:

FourAs the home window was closed it is obvious that the 6 candles the were not extinguished were lit till they melted far entirely. Therefore only 4 candles that were extinguished continue to be at the end.

Mind Teasers :Most renowned Logical Puzzle

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Outside a room there space three light switches. One of switch is linked to a light pear inside the room.Each that the three switches deserve to be one of two people "ON" or "OFF".You are allowed to set each move the method you desire it and also then enter the room(note: girlfriend can enter the room only once)Your task is come then recognize which move controls the bulb ??
Solution:

Set the first switches on for abt 10min, and also then switch on the 2nd switch and then go into the room.

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Three cases are possible1.Bulb is on => 2nd switch is the ans2.Bulb is off and also on emotional bulb , girlfriend will discover bulb to be warm=>1st switch is the ans.3.Bulb is off and on touching 2nd bulb , girlfriend will discover bulb to be normal(not warm)=>3rd bulb is the ans.