Mental Marathon Questions

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<p>Team .......................</p> <p>Question 1: Connect the 9 dots with 4 straight lines. Don't cross the same dot twice.</p> <p>. . .</p> <p>. . .</p> <p>. . .</p> <p>Team .......................</p> <p>Question 2: The 10" pizza sells for $ 4.99 at my favourite pizza store. The store claims they have a great deal on the large 14" pizza, which is specially priced at $ 7.82. What is the per cent discount the store is offering?</p> <p>Team .......................</p> <p>Question 3: In a recent motor ride it was found that we had gone at the rate of ten miles an hour, but we did the return journey over the same route, owing to the roads being more clear of traffic, at fifteen miles an hour. What was our average speed?</p> <p>Team .......................</p> <p>Question 4: There was a small lake, around which four poor men built their cottages. Four rich men afterwards built their mansions, as shown in the illustration, and they wished to have the lake to themselves, so they instructed a builder to put up the shortest possible wall that would exclude the cottagers, but give themselves free access to the lake. How was the wall to be built?</p> <p>Team .......................</p> <p>Question 5: Hiram B. Judkins, a cattle-dealer of Texas, had five droves of animals, consisting of oxen, pigs, and sheep, with the same number of animals in each drove. One morning he sold all that he had to eight dealers. Each dealer bought the same number of animals, paying seventeen dollars for each ox, four dollars for each pig, and two dollars for each sheep; and Hiram received in all three hundred and one dollars. What is the greatest number of animals he could have had? And how many would there be of each kind?</p> <p>Team .......................</p> <p>Question 6: The illustration is a prison of sixteen cells. The locations of the ten prisoners will be seen. The jailer has queer superstitions about odd and even numbers, and he wants to rearrange the ten prisoners so that there shall be as many even rows of men, vertically, horizontally, and diagonally, as possible. At present it will be seen, as indicated by the arrows, that there are only twelve such rows of 2 and 4. The greatest number of such rows that is possible is sixteen. But the jailer only allows four men to be removed to other cells, and informs me that, as the man who is seated in the bottom right-hand corner is infirm, he must not be moved. How are we to get those sixteen rows of even numbers under such conditions?</p> <p>Team .......................</p> <p>Question 7: 999999999999999 = 1990 Insert +, -, x or / in suitable places on the left side of = so as to make the equation true:</p> <p>Team .......................</p> <p>Question 8: A gang of 17 thieves steals a bag of gold coins. In t rying to share the coins equally, there are three coins remaining. In the ensuing fight over these three coins, one of the gang members is killed. In the next attempt to equally distribute the coins, there are 10 coins remaining. Again the gang fights, and another member dies. The third attempt is successful. What is the smallest number of coins stolen?</p> <p>Team .......................</p> <p>Question 9: Mr. and Mrs. Ford have three daughters. When the youngest was born, you could multiply the middle childs age by three to get the oldest sisters age. Nine years ago, you could add the middle childs age to the youngest childs age to get the oldest childs age. What is the youngest that the oldest child can be now?</p> <p>Team .......................</p> <p>Question 10: Consider a vertical wheel of radius 10 cm. Now suppose a smaller wheel of radius 2 cm, is made to roll around the larger wheel in the same vertical plane while the larger wheel remains fixed. What is the total number of rotations the smaller wheel makes when its center makes one complete rotation about the larger wheel?</p> <p>Team .......................</p> <p>Question 11: A snail wants to creep on to the top of the tree 5m high. During the day it can creep up 3m but during the night it creeps down 2m. How many days does it need to reach the top?</p> <p>Team .......................</p> <p>Question 12: Steve has three piles of sand and Mike has four piles of sand. If they put them all together, how many do they have?</p> <p>Team .......................</p> <p>Question 13: Two drivers are going to the next town which is 100 miles away. They depart at the same time, however the first driver stops for gas during the first 50 miles, the second driver stops during the second half. Each stop takes 10 minutes. They both drive with the same speed 60 mph during the first 50 miles and 65 mph during the second half. Who, do you think, arrives first?</p> <p>Team .......................</p> <p>Question 14: A man is running across a bridge. When he is 3/8 of the way across, he heard a train coming behind him. If he keeps running he will reach the end of the bridge at the same time with the train. If he turns around and runs back, he will get to the beginning of the bridge at the same time with the train. The man runs at a speed of 5mph. What is the speed of the train?</p> <p>Team .......................</p> <p>Question 15: There is a large cube that is composed of small sugar cubes. The large cube is 10 sugar cubes long, by 10 sugar cubes wide, by 10 sugar cubes high. How many sugar cubes are on the surface of the large cube?</p> <p>Team .......................</p> <p>Question 16: A rope ladder hangs over the side of a ship. The rungs are one foot apart and the ladder is 12 feet long. The tide is rising at four inches an hour. How long will it take before the first four rungs of the ladder are underwater?</p> <p>Team .......................</p> <p>Question 17: How many 3-cent stamps are there in a dozen?</p> <p>Team .......................</p> <p>Question 18: How can you throw a golf ball with all your might and -- without hitting a wall or any other obstruction -- have the ball stop and come right back to you?</p> <p>Team .......................</p> <p>Question 19:</p> <p>Place a different number in each of the ten squares so that the sum of the squares of any two adjacent numbers shall be equal to the sum of the squares of the two numbers diametrically opposite to them. The four numbers placed, as examples, must stand as they are. The square of 16 is 256, and the square of 2 is 4. Add these together, and the result is 260. Alsothe square of 14 is 196, and the square of 8 is 64. These together also make 260. Now, in precisely the same way, B and C should be equal to G and H (the sum will not necessarily be 260), A and K to F and E, H and I to C and D, and so on, with any two adjoining squares in the circle. All you have to do is to fill in the remaining six nu mbers. Fractions are not allowed, and no number need contain more than two figures.</p> <p>Team .......................</p> <p>Question 20: How can you arrange for two people to stand on the same piece of newspaper and yet be unable to touch each other without stepping off the newspaper?</p> <p>Team .......................</p> <p>Question 21: Of the 100 people at a recent party, 90 spoke English, 80 spoke Hindi, and 75 spoke Filipino. At least how many spoke all three languages?</p> <p>Team .......................</p> <p>Question 22: The diabolical Dr. Nasty has turned his Growth Ray on a perfect cube that used to measure one metre on a side. The new larger cube has twice the surface area of the original. Find the volume of the larger cube.</p> <p>Team .......................</p> <p>Question 23: In which direction is the bus pictured below travelling?</p> <p>Team .......................</p> <p>Question 24: How many fs are there in the following sentence? Finished files are the result of years of scientific study combined with the experience of years of dedication.</p> <p>Team .......................</p> <p>Question 25: Which figure should be placed in the empty triangle?</p> <p>Team .......................</p> <p>Question 26: Start at the center number and collect another four numbers by following the paths shown (and not going back -wards). Add the five numbers together. What is the lowest number you can score?</p> <p>Team .......................</p> <p>Question 27: The area of a square is equal to the square of the length of one side. So, for example, a square with side length 3 has area (3 2), or 9. What is the area of a square whose diagonal is length 5?</p> <p>Team .......................</p> <p>Question 28: I travelled from Dubai to Abu Dhabi last week at 60 miles per hour, I had filled my petrol tank just before I left, so it was full with 25 gallons. Unfortunately, my petrol tank sprang a leak immediately and I only managed to drive 300 miles before I ran out of petrol. My car does 30 miles per gallon, how fast was I losing petrol through the hole?</p> <p>Team .......................</p> <p>Question 29: Homer had suffered a bizarre accident that affected his eyesight. The doctor said it would be temporary, but for the next 4 weeks, he had to adjust how he did some things. The accident had affected his focal length. He was only able to focus on objects that were 6 or more feet away from him, anything closer than 6 feet was just a blur. Homer was used to shaving up close in front of his bathroom mirror. Now after the accident, how close could Homer get to the mirror to see his face clearly enough to shave?</p> <p>Team .......................</p> <p>Question 30: The island of Elbonia have a rather eccentric postal system. Postage for an item can be anything from 1 dinar to 15 dina ri, and you must use exact postage. Frustratingly, there is only space on the envelopes in Elbonia to attach a maximum of three stamps. What is more, they only have three different denominations of stamps; can you work out what they are?</p> <p>Team .......................</p> <p>Question 31: My local bus company has recently expanded and no longer has enough room for all of its buses. Twelve of their buses have to be stored outside. If they decide to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company currently own?</p> <p>Team .......................</p> <p>Question 32: A man in a restaurant asked a waiter for a juice glass, a dinner plate, water, a match, and a lemon wedge. The man poured enough water onto the plate to cover it. "If you can get the water on the plate into this glass without touching or moving this plate, I will give you $100," the man said. "You can use the match and lemon to d o this." A few minutes later, the waiter walked away with $100 in his pocket. How did the waiter get the water into the glass?</p> <p>Team .......................</p> <p>Question 33: If you balanced a broom horizontally on your finger, so that your finger was exactly on the broom's center of gravity, marked that spot and cut the broom in two, then you would have a long and a short piece. The long piece being most of the handle and the short piece being the bristle end and a small part of the handle. Now what will happ en if you weigh both pieces?</p> <p>Team .......................</p> <p>Question 34:</p> <p>A cylinder 72 cm high has a circumference of 24 cm. A string makes exactly 4 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?</p> <p>Team .......................</p> <p>Question 35:</p> <p>In the above figure, the rectangle at the corner measures 5 cm x 10 cm. What is the radius of the circle in cm?</p> <p>Team .......................</p> <p>Question 36: A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 4 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours. What fraction of the tank (initially empty) will be filled in 0.57 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75 )</p> <p>Team .......................</p> <p>Question 37: Two trains, 200 km apart, are moving toward each other at the speed of 50 km/hour each. A fly takes off from one train flying straight toward the other at the speed of 75 km/hour. Having reached the other train, the fly bounces off it and flies back to the first train. The fly repeats the trip until the trains collide and the bug is squashed. What distance has the fly travelled until its death?</p> <p>Team .......................</p> <p>Question 38:</p> <p>Our friend Steve in the illustration has a large sheet of zinc, measuring (before cutting) 2.4m by 0.9m, and he has cut out square pieces (all of the same size) from the four corners and now proposes to fold up the sides, solder the edges, and make a cistern. But the point that puzzles him is this: Has he cut out those square pieces of the correct size in order that the cistern may hold the greatest possible quantity of water? You see, if you cut them very small you get a very shallow cistern; if you cut them large you get a tall and slender one. It is all a question of finding a way of cutting put these four square pieces exactly the right size. What size do the squares in the corners need to be to achieve the largest cistern size?</p> <p>Team .......................</p> <p>Question 39: There is a river with an island and five bridges. On one side of the river is Sheik Mos palace, and on the other side is Sheik Mo in the foreground. Sheik Mo has decided that he will cross every bridge once, and only once, on his return to the palace. This is, of course, quite easy to do, but on the way he thought to himself, "I wonder how many different routes there are from which I might have selected."</p> <p>Determine how many different routes are possible.</p> <p>Team .......................</p> <p>Question 40: The diagram represents the streets in a development of villas. Every street, A to B, B to C, C to H, H to I, and so on, is 100 metres in length. There are thirty-one of these streets. Ashish and a DM official have to inspect all of them, starting and finishing at point A. Being above 42 degrees outside they want to take the shorted route possible. Determine the shortest route and how far they must travel.</p> <p>Team .......................</p> <p>Question 41: The crescent is formed by two circles, and C is the centre of the larger circle. The width of the crescent between B and D is 9 inches, and between E and F 5 inches. What are the diameters of the two circles?</p> <p>Team .......................</p> <p>Question 42: Brian, in the illustration, wants to cut the piece of wood into as few pieces as possible to form a square table-top, without any waste of material. How many pieces would you require? And of what shape?</p> <p>Team .......................</p> <p>Question 42.2: The Pierrot in the illustration is standing in a posture that represents the sign of multiplication. He is indicating the peculiar fact that 15 multiplied by 93 produces exactly the same figures (1,395), differently arranged. The puzzle is to take any four digits you like (all different) and similarly arrange them so that the number formed on one side of the Pierrot when m...</p>