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Tickle Your Grey Cells

Puzzle corner is a dedicated section for honing analytical, mathematical and reasoning skills. In this section every week you will find five Puzzles. Theses mind twisters have been carefully selected after a thorough research and provide right inputs for tickling your grey cells. Solving puzzles is considered very good exercise so as to remain mentally active. Puzzle solving enhances memory and processing speed.

Puzzle is one of the most popular category in competitive examinations. All the major Indian MBA entrance exams like CAT, MAT, XAT and SNAP have direct questions or questions based on similar logics in written test. Besides MBA exams, competitive exams like GRE, GMAT, Bank PO, SSC & other government exams include puzzle questions. Most of the companies while recruiting through campus includes Puzzles in the written tests or at interview stage. Hence those who are preparing for campus placement tests this section is a must.

Week of the Year 

An auditorium is 6 meters high, 20 meters long and 5 meters wide. A fly is present in the middle of one of the end walls (5 X 6 meters), one meter below the ceiling. In the middle of the other end wall one meter above the floor, a lizard wants to catch the fly. Find out the the shortest way for the lizard to catchhold its prey?
 
Generally most of the readers will answer this as (1 + 20 + 5) = 26 meters. Some may think of a path passing through the diagonal along the long wall and width and consequently get the answer as 25.3 metres. However, much shorter path is available and this is one along which, amazingly, the lizard will have to crawl over five (of the six) sides of the room.
 
 
The six sides of the room (including the floor and the ceiling) can be opened out into a plane surface. (In order to visualize this the reader is advised to imagine the process of opening out a cardboard box). When the room is considered as the development of this particular surface, straight line between the two points X and Y, which correspond to the positions of the lizard and the fly respectively, gives the shortest path.This path, being formed by the hypotenuse of a triangle whose sides are 22 and 11 meters, would be the square root of (222 + 112) or 24.6 meters long and traverses five sides of the auditorium, i.e. one end wall- the floor – a long wall- the ceiling- the other end wall.

Can you name the biggest number that can be written with two 1's and two 0's?
People often think of the number 1100 as the biggest number that can be written with two 1’s and two 0's.
But there is a number many, many times greater than this number, namely: 1010
In fact, 1010 is almost ten million times greater than 1100.

The President decides to give a prisoner, who is about to be sentenced to death, one last chance to live. There are 2 doors, one - the life door and the other - the death door. There is one security person standing by each door, who knows about the doors. However, one of them always tells the truth and the other always tells a lie. There is no way to identify which door is the life door and which is the death door. There is no way to distinguish which security person is telling the truth. The prisoner can only ask only one question from any of the security person. After this he needs to choose a door. If he walks in the death door, then he will be executed. If he walks in the life door, he will get a life. He did choose the life door and lived. What was the question he asked? How did he choose the door after he got the answer from one of the security person?
Assume the security person X is by door X and the other person is by door Y. Let the prisoner go to person X and asks this question "If I ask person Y what door is door Y, then what will be answer given by him: life door or death door?"
If the answer is life door (door X), he can walk in the door Y. If the answer is death door (door Y), he can choose the door Y and walk in. This is because the question goes through 2 levels of questions from 2 people. The overall answer will be always a lie because there is always one person lying and the other telling the truth.

The LAZY express runs between P & Q. For the up as well as the down journey, the train leaves the starting station at 6 AM everyday & reaches its destination at 7 AM after 3 days. Mr. Jain once traveled by Lazy Express from Q to P. How many trains by the same name did he cross en route?
Mr. Jain crosses exactly seven trains on the route - 3 trains which had already started before the start of Mr. Jain while 4 trains will be those which started after the start of Mr. Jain.

The following set of boxes has to be filled in such a way that all the odd digits are utilized in the boxes on the left side while even digits are utilized on the right side boxes. The digits available are: 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make the equation correct.
 

The following are the two different solutions to this problem where all odd & even digits are placed in left & right boxes respectively.
The sum of the integers on the left side is always ODD as it is the sum of three odd numbers While on the right hand side since the two digit number has to be even so the remaining part should be odd and that can be formed in only one way i.e 6 / 2 = 3
 

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