Difficult Mathematical Puzzles - 3

Mathematical riddles and puzzles are frequently asked in various competitive exams. These are based on the basic concepts of probability, arithmetic, ratio & proportion, time & distance, etc. Here is a compilation of mathematical puzzles grouped into: easy, medium and difficult puzzles. Each article contains a set of 10 maths puzzles with answers. In this article, you will come across difficult maths puzzles devised to hone your mental aptitude.
Solve the given questions and check your mental abilities:
Q.1. 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?
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Q.2. In 1991, a devastating flood ravaged many districts of Bihar. A group of villagers found itself confronted by a wide and deep flood water. However, they found two children who were rowing a boat. But the boat was so small that it can only carry either the 2 children, or 1 adult person and it can be rowed by single child or adult. Can the 246 villagers move across the flood water? If yes, what is the minimum number of movements that the boat has to make from shore to shore?
Q.3. On a chessboard, one can choose 2 squares at random . According to you, what is the probability that they have a common side?
Q.4. There are 12 identical balls having exactly equal weight except one ball which is heavier than the other 11 balls. How many minimum weighings are required to identify this different ball by a simple weighing balance?
Q.5. P Q R
        T U V
Each of the digits 1,2,3,4,5,6,7,8, and 9 is:
i. Represented by a different letter in the figure above.
ii. Positioned in the figure above so that each of P+Q+R, R+S+T, T+U+V, and V+W+X is equal to 13.
Which digit does T represent?
Q.6. Khurana would like to take a new apartment on rent. The owner asks him: "Please tell me how many children you have." Khurana answers: "I have three of them." The owner: "What are the ages of your children?". He answers: "The product of the ages is equal to 72." The owner replies: "This is not enough information dear!". "Sorry that I was a little bit unclear, but the sum of the ages is equal to the house number in front of your apartment," says Khurana. The owner: "This still isn't enough information!". Khurana replies: "My oldest child loves chocolate." The owner: "Thanks for your cooperation, I now know the ages." Are you as smart as the owner? Then give the ages of the children.
Q.7. Ramlakhan, while leaving for school looks at the clock in the mirror. Since the clock has no number indication, he makes a mistake in interpreting the time. Assuming the clock must be out of order, he cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is four and a half hours later than the time that Ramlakhan saw on the clock at home. At what time did he reach school?
Q.8. What is the minimum number of weighing operations required to measure 31 kg of wheat if only one weight of 1 kg is available?
Q.9. Mr. Ravinder Gulati has 3 timepieces in his house - a wall clock, an alarm clock and a wristwatch. The wrist watch is always accurate, whereas the wall clock gains 2 minutes every day and the alarm clock loses 2 minutes every day. At exactly midnight last night, all three watches were showing the same time. If today is 23 July 2007, then on which date all three clocks will show the same time again?
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Q.10. There are 3 persons- A, B and C. On some day, A lent tractors to B and C as many as they had. After a month B gave as many tractors to A and C as many as they have. After a month C did the same thing. At the end of this transaction each one of them had 16. Find the tractors each originally had?
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