Transcripts
1. Welcome: Hello guys. Welcome to the five-minute puzzle series. In this series we are going to talk about some of the most commonly asked puzzles in the interviews. These puzzles might look trivial to you, but if you find the caveat in them, then you are definitely going to leave a positive impression on the interviewer. This is not a sequential course. where you need to go step-by-step and follow all the videos. Rather you can start from any video in the series. Each of the puzzle might take around five minutes to solve. I highly recommend you to pause the video once you understand the problem and then try to solve it for yourself. This would help you in better understanding the problem, and will definitely improve your problem-solving skills. So let's get started without much ado.
5. 25 Horses Puzzle: Hello there. Let's try to solve this puzzle. There are 25 horses and only five race tracks. Only one horse can run on a particular track. So that means only five forces can perform the race at any given point in time. You need to find out the minimum number of races that would be required to find the fastest three horses from among 25 horses. So Let's try to solve this puzzle. As we have only five race tracks, we can only allow five horses to run simultaneously. And we don't have any timer or a clock to measure the running times. We can group the horses in the batch of five. Therefore, we will be having five groups. Naming group A, group B, group C, D, and E. We mark the horses with the batch and the rank in the batch. So let's try to visualize the races. In the race of group A Let's say A1 comes first. A2 finishes on second position. A3 finishes at third position. Similarly, A4 and A5 finish at fourth, fifth positions. Similarly, in the race of group B, B1 comes first, and B5 finishes at the fifth position. In the race of group C. C1 finishes first, C2 finishes second. And so on. In the race of group D, and D1 finishes first, D2 second, D3 on third position, D4 at fourth And D5 at five position. In our fifth race of group E, E1 finishes at first position, E2 at position two, and so on. So after the first five races, we have the following stats. Now we can eliminate the fourth and the fifth row, because only three fastest horses are required. Now, we need to have the sixth race. where the winner from each group will compete with each other. So here, the race would be between A1, B1, C1, D1, and E1. Let's assume A1 finished first and B1 finished second. C1 finished third. D1, finished fourth, and E1 finished at fifth position. Now, from the six race, we can eliminate the fourth and the fifth column. Because if C1 is the third fastest horse in the sixth race, then D1, D2, D3, and E1, E2, E33 could not be second or the third fastest horse. So we can eliminate them. Now as A1 came first in the race of all the winners from each group, we can conclude that even is the fastest horse. So we do not need to include it in any other race, so we can eliminate it. Now. We are left with A2, A3, B1, B2, B3, C1, C2, and C3. A total of eight horses. But we can only allow five forces to run simultaneously. So for the next race, we need to eliminate three horses. From the sixth race, we know that C1 is the third fastest horse in that batch. So C2 and C3 can be eliminated as they cannot be the third fastest horse. Now, we are left with A2, A3, B1, B2, B3, and C1, that is six horses. Let's see if we could eliminate 1 horse. And then we will be having the required Five horses. for our next race. Now since A1 is the fastest horse, let's look at the second fastest horse. The second fastest horse could be B1 or A2. Because A1 as faster than B1, B1 is faster than B2, and B1 is also faster than C1. So B1, A2 could be the second fastest horse. Now let's look at the case If B1 is the second fastest horse. If B1 is the second fastest horse, the third fastest horse could be A2, B2, C1. And if A2 is the second fastest horse, the third fastest horse could be A3, B1, C1. So this means we can eliminate B3 because it will surely not be the third fastest horse, Know we are left with A2, A3, B1, B2, and C1, we can have a race between these five horses and we will for sure, know the second fastest and the third fastest tours, because the fastest horse in the seventh race would be the second fastest horse from amongst that 25 horses. And the second fastest horse from the seventh race would be our third fastest horse from among the 25 horses. So that means in total, we need seven races. You'll find the three fastest horse from these 25 horses.
6. 3 Friends & 1 Motorbike Puzzle: Let's start with another puzzle. Suppose there are three friends who wish to visit their other friend located in another city, which is exactly 300 kilometers away. The three friends have a motorbike which has a seating capacity of 2 people at any point of time. The speed of the motorbike is 60 kilometres per hour. Again, each of the guy can walk with a constant speed of 15 kilometers per hour. You need to figure out the minimum amount of time required by the 3 friends to reach the other friend in another city. Let's say the three frames Alex, Ben. And Carl decided to go to their friend's house, which is exactly 300 kilometers away from their location. And they have a motorbike which can accommodate only two people. So let's look at the solution. The immediate answer to the puzzle is that the two friends, will use the motorbike and Alex will start walking towards the destination. Once, Ben & carl on the motorbike, reach the destination Ben will drop Carl and then start moving back to pick Alex and bring him to the destination. Let's say Alex reaches point X. When Ben & Carl on the motorbike reaches the destination. Time Taken by Alex to each point X is equal to the time taken by Ben to reach the destination. We know that time is equal to distance divided by speed. So let's say Alex covers a distance of m units with a speed of 15 kilometers, both Ben & Carl covers a distance of 300 kilometers with a speed of 60 kilometers. with the help of a motorbike. So this is equivalent to five. So m is equal to 5 times 15, which is equal to 75. So that means Alex covers a distance of 75 kilometers. Then Vin and gull reaches the destination, then drops off girl at the destination and starts moving back to pick Alex. Let's say they meet at bind divide. It'll point why? Alex has covered a distance of d units, some point x. So this means men has covered 225 minus d kilometers. Because the total distance is 300 kilometers and it'll point x, it's 75 kilometers. So from point X, the destination is 225 kilometer survey. And the distance between x and y is d u, d kilometers. So that means from point dry, the destination is 225 minus d kilometers. Now, time taken by Alex to reach point y is equal to the time taken by Ben on the bike for each point y from the destination. So now here, Alex covers a distance of three units with the speed of 15 kilometers. And then covers a distance of 225 kilo ohm minus 225 minus d kilometers, that the speed of 60 kilometers. So solving this, we get d is equal to 45 kilometers. This means that Alex has covered a distance of 45 kilometers. And Ben has covered a distance of 180 kilometers. Now that we know all the distances covered by the friends, let's try to calculate the time. So Alex covers 75 kilometers on foot with the speed of 15 kilometers, but R. So this means 75 by 15, which is five hours. So Alex takes five hours to reach point x. He further moves 45 kilometers from point X to Y, then X m. So this is again 45 by 15 because he's moving speed is 15 kilometers. This leaves us with three hours. And finally, they cover the rest, 180 kilometers on bike with a speed of 60 kilometers per hour. So that means three hours on bike. So the total time taken by the friends to reach the destination is 5 plus 3, plus 3, that is 11 hours. So if the friend decided to break the Janine this way, they will require 11 hours to reach the destination. Now, this is obviously not an optimized solution because after dropping Carl, men and Alex are still performing some work while girl is sitting idle. Now, we can optimize the solution further by dropping curl at the point before destination so that all the friends are performing some work and nobody is sitting idle. This will surely reduce the total time taken by difference. So let's see that approach. Now. Enter optimized solution. Let's say Alex reaches point x, then men drops curl at point P. Let's assume men and GL on the bike covers a distance of p kilometers, ill point P. And Alex covers a distance of y kilometers, ill point x. After dropping girl at point P, then starts moving back to pick Alex. Let's see, Alex and been made at point by during this time, both Alex and guide has covered a distance of d and x because devoting speed of all the trends is seen. And let's see, Ben has covered a distance of n kilometers to meet alex at 0.5. So the time taken by Alex and been to reach point y would be same. Alex colors and distance of legal meters. And the speed of 15 kilometers, distance of n kilometers, minute speed of 60 kilometers. So this gives us a relation. N is equal to the demand, the initial distance covered by Alex point x as y kilometers, and the initial distance covered by Ben and Carl, L point P as P kilometers. And we know that the time taken by Alex to reach point x from the start was equal to the time taken by Ben and Carl to reach point P. So we can see that by 15, because Alex was working, is equal to E by 16, because the speed of the bike is 60 kilometers and the initial distance was picometers. Now from here, we can see that b is equal to y plus d plus n. And we have recently seen that n is equal to 40. So this gives us By plus B plus 4D, which is equal to y plus 5 b. So substituting the value of b here gives us divided by 15 is equal to 53 by 60. This leaves us with the equation, y is equal to five by three times d. So this is our second equation. Now we need to find the distance which garden needs to travel from point is such that both Ben and Alex on bike and girl on fault reaches the destination at the same time. So let's say Alex and been rebels M kilometers from point y. Whereas the garden travels a distance of Zen kilometers from point to the destination. Now the all should reach the destination at the same time. This means that the time taken by God to reach the destination from Point S is equal to the time taken by Alex and been on bike to reach the destination from point vi. Zed is the distance covered by Carl on foot with 15 kilometers. But this gives us the time taken by Carl should be equal to M by 16. Now, we know that the distance between point a and t is equal to 4 times d from our first equation. So m is equivalent to 4D plus D plus zed, which is equal to five plus 0. So substituting the value of m here gives us then by 15 is equal to 5 b plus by 16. Solving this gives us a relation that zed is equal to five by three times d. From our second equation. Vino, that the initial distance covered by Alex, which was marked by is equal to 5 by 3 D. So the total distance is equal to 300 kilometers, is equal to Vi plus B plus 4D plus B plus z. Now substituting the values of y and z and we get 300 equal to five by three. B plus B plus 4D plus b plus 5 by 3 times B. This is equivalent to 28 divided by three times b. So solving this, we get b is equal to 32 point 14 kilometers. Now, we can calculate the values for all the distances covered by Alex, Ben, and GL respectively. So this initial distance is equivalent to 53, 56. This is 32 point. Been for 40 is equivalent to 128, 56, this is 32 point and 14. Then again, this is 53.56. Now it's time to calculate the total time. So Alex covers 53, 56 kilometers with a speed of 15 kilometers. So this gives us 3.57 hours. Then Alex further travels 32.14 kilometers, speed of 15 kilometers, which gives us 2.14 hours. And then Ben picks up Alex and reaches the destination along with God by covering a total distance of m units, which is equivalent to 128.56 plus 32, 24 plus 53.56 kilometers, that the speed of 60 kilometers per hour. So this gives us another three-point, seven hours. So the total time taken by the friends to reach the destination is equivalent to 3.57 plus 2.214 plus 3.57 hours, which is equivalent to 9.28 hours. Now, this is the optimized solution. Following this approach, the friends can reach the destination and 9.8 hours.