Maths And Logic Puzzles

These puzzles need basic math and logic. Some of them also need understanding of compound interest, area and volume of cubes, formulas for Newton's laws of motion (velocity, acceleration, distance: v=u+at, s=ut+0.5at^2) and basic algebra. Maths knowledge is needed at class 8 level (13 to 14 years age) though it is quite possible that older students or adults with maths and science majors may find some of these puzzles challenging. Each problem is supposed to be completed in 3 to 10 minutes.

• I am traveling by commercial jet plane at an altitude of 12000m and from my window I see another plane which is at 8000m altitude. Initially the distance between the 2 planes is 4km (say if the two planes were tied to ends of a chord, the length of that cord would be the distance). After 10 seconds, the distance between the planes is 7km. Both the planes are traveling at 900 kmph. All figures are exact, no approximations. Is this possible or are there issues in the problem? Both planes retain their altitude during the period mentioned above.

  

• A magician says he can escape from a cement enclosure in 2 minutes in which he is “buried”. To verify his assertion, he is asked to remain standing and cement is poured over and around him so that there is a cube of cement (2m each side), He is buried completely inside the cube of cement. He is 6’ tall with a chest size of 42” and weighs 80 kg. His body has a density of 0.985 gm/cc. What was the weight of cement in the cube (before he escapes)? If you need any information that is not provided, then assume values x, y etc and provide your answer in terms of the assumed values.

  

• Two cows standing 120m apart in east west direction start charging towards each other (one going east and other going west) at 10AM at the rate of 1m/s and 2m/s. There are two flies, one sitting on each cow's left horn and they start (one towards east and one towards west) at a speed of 0.5m/s at 10AM. At what time do the flies meet? (There are 2 answers)

  

• I have a huge pack of coins valued at about Rs20,000 consisting, equally in value,  of the following types of coins:  Rs1 (P gm each), 50p (Q gm each) and 25p (R gm each). I want to courier Rs 200 worth of coins to my friend who is in Jeypore, Orissa. The courier says it will cost Rs 100 up to 50gm and Rs 2 for each additional gm. Assuming I can send any combination of coins to my friend and I want to minimize courier charge, what will my cost to courier the coins? 

• We all know how to add numbers.. Let's say we have many 7 digit numbers and we want to add them all up. We would usually sum the units digit then tens and so on, from right to left. What would be the advantage of counting from the left to the right? Of course we will assume that numbers are always right aligned before we start adding –whether we add from the left or from the right. 

• Vivek express starts from Dibrugarh in Assam to Kanyakumari once every day in each direction. This is about 4000km and the avg speed is 50 kmph. What is the min number of rakes needed to cater to this train? A rake is the set of all 20 or so compartments including pantry car, engine, guard van etc that make up a train. Assume that rakes for Vivek express are not shared with any other train - the rakes are dedicated for that train only. Departure time is the same on all days of the week. Assume the trains always arrive on time. Departure time in Dibrugarh and departure time in Kanyakumari may not be the same.

• A particular family tree was analyzed for “n” generations starting from Adamosamy who was the earliest known member. There were 3 offspring for each set of parents. Every person married and had children. Each set of parents divided their wealth equally among all their children. If each person in the family (from Adamosamy to nth generation) inherited the same amount of money from the respective parents, what can you conclude about the earning / inheritance / expenditure of each scion (member) in that family tree? 

• This is a scene from the movie: Enemy At The Gates – a man shooting a person who is jumping over a ledge/broken corridor: A part of a corridor has been bombed by the Germans. A Russian has to jump across the broken corridor. A German sniper is sitting with his rifle in such a way that he can see only the broken part of the corridor. Both men are at the same height above the ground. The German can see the Russian while the latter is jumping and will try to shoot the Russian down. Before he jumps and after he has landed on the other side of the corridor, the Russian is safe from the sniper (shooter) – as the corridor is covered. Bullet velocity 200m/s, Distance of corridor from sniper 100m, Length of broken corridor: 5m, horizontal velocity of the Russian across broken corridor as he is jumping = 8m/s, What is the min and max length of broken corridor so the sniper can shoot the Russian (a notional distance of 5m is given to provide a perspective)? Disregard effect of gravity and friction in calculations.

• I plan to buy 10,000 sq ft of land at Rs 3000 per sq ft. And I plan to fence my property at Rs 20 per ft. I can buy the property in any shape. What will be cost of fencing if my primary consideration is to minimize the fencing cost? Exact answer not needed. Just give the right expression and explanation.

• 7^a +6^b = 5^c where a,b,c are integers and ^ refers to exponentiation. For what kind of values of a,b,c is this equality definitely not possible? Give reasons. 

• The cost of a passenger plane is $120million. 40% of the cost was financed through a bank loan @10% compound interest to be repaid in 10 years in equal yearly installments. Cost of fuel: Rs 50/liter, fuel efficiency: 3.5liter/km, 120 seats. 7 Air crew: each aircrew costing Rs 1000/hr. Avg flight speed = 800kmph. Cost of fuel is 50% of total costs of running an airline. 1 USD = Rs60. In a 1500km long flight what should be the avg price per seat for airline to make 10% profit? List any assumptions you need to make. 

  

• I plan to divide all my money equally among my relatives. Unfortunately I am not sure how many relatives I have (maybe 10 or even 190 – note that these are the number of my relatives and not just number of my children). I am pretty sure my wealth is about 3-4 crores - again I don't know exactly how much.. I tell my lawyer to draw up a will, leaving my entire money to be divided equally among my relatives and any balance from my estate to be given to the lawyer as his fees. No matter what MNR is, the lawyer’s fee will remain the same. Meaning the kitty for my relatives is constant - regardless of whether the number of relatives I have is 1 or 2 or … the max number of relatives (MNR). My lawyer says he doesn’t know how to handle this since I don’t know the number of relatives nor the extent of my own wealth.. I tell him "Ok, assume I have Rs 3 Crores only. What will be the value of MNR I can leave my money to?" Meaning so long as the number of my relatives is any number up to that max, my money (a fixed amount) can be divided equally among them and balance (also a fixed amount) given to lawyer. If after my death there happen to be more relatives than MNR, the lawyer will use his discretion and restrict the number to MNR. In such a case, some of my relatives won’t get any money. NOTE: MNR is decided at the time of writing the will regardless of the actual number of relatives I may actually have. NOW THE QUESTION TO YOU IS ONLY THIS: Which person got the max money from my estate and how much was it approximately?  (1crore = 10 million) Answer needs explanation.