Added: Talisha Grabowski - Date: 09.11.2021 00:58 - Views: 28822 - Clicks: 9645
In this improved solution to Einstein's puzzle, learn how to find the answer to Einstein riddle Who owns the fish confidently and systematically. Briefly, five nationals of five different countries live in five differently colored houses, keep five different pets, drink five different fluids and smoke five different brands of cigarette. In 20 minutes time analyzing as many as 15 given conditions, you have to answer—who owns the fish? Not easy at all but not too difficult also. It is a joy solving this very well-formed reasoning puzzle. After solving it more than one and half years back, by chance I discovered that the puzzle is the popularly known Einstein's puzzle or Einstein's riddle.
You may go through this earlier straightforward solution in the following link,. Method based solution to Einstein's logic analysis puzzle whose fish. A few months ago as I went through this earlier solution, I couldn't but ignore a few blemishes. In this session I have removed these shortcomings and explained the new solution as clearly as possible. I have used terminologies for strategies, techniques and methods used in solving the puzzle, but also explained why the techniques are effective and how the methods are to be used.
Goal is — anyone of you should be able to understand how the problem is solved and learn to use the strategies, techniques and methods and if possible—improve these. Expected outcome—your interest and involvement. Let's proceed by first stating the problem and going through the systematic solution step by step.
Can you find out in 20 minutes? Well, that is the standard time limit for this puzzle. If you have time in your hands, go on till you solve it. This is one of the most well-balanced puzzles I know of and I am sure you will enjoy when trying to solve it. There are six variables or dimensions as I call it in this problem— House each with a specific position, Color of house, Occupant each with a specific nationality, Pet, Drink choice, and Smoking choice. Each of these variables has five unique values. Assuming that this is a well-formed logic puzzle with a unique solution, we understand by a brief scan through the problem description, that when fully ased, there will finally be five unique combinations of values of six variables.
In other words, values of the six variables five for each variable have to be ased one-to-one. Simply speaking, no single variable value can be ased to two values of another variable. For example, an occupant of a specific nationality living in a house of a fixed position of unique color , has a unique pet , drinks a unique drink and smokes a unique brand of cigarette. Thus the problem involves one to one asment between six sets of variable values.
The one-to-one asment property makes solution simpler. The Swede living in blue house on the rightmost position smokes Dunhill, drinks beer and keeps dogs as pets. Though the problem was to find whose pet is the fish, a specific single goal, it may turn out that while the asments are carried out systematically through logic analysis, the whole of the logic table may get fully ased, thus automatically giving the solution.
At first glance the logic puzzle may seem daunting unless the problem solver is naturally gifted or used to logic analysis of various forms. We need to analyze the fifteen given logic statements to find out who owns the pet fish. These statements are also called logic statements, and this kind of problem, reasoning and logic analysis puzzle. While we analyze the 15 logic statements one by one, we need to write down the at every step so that we can analyze the next logic statement along with the of analysis achieved thus far.
Gradually the will get more enriched and move towards the solution. To write down the of logic analysis up to any stage, we will use the most compact logic representation in the form of fully collapsed column logic table with five columns and five rows. The houses identified by their positions form natural column labels with position embedded in each. The other five variable names form the row labels. For example, the column labels will be from left to right—House 1, House 2, House 3, House 4 and House 5 with House 1 being the leftmost and the first house and House 3 being the center house.
Note: At first it may seem occupant should be the column header. But asing house as the primary variable is more natural , as from the logic statements we find each house has a fixed relative position with each other. This relative position property of a house simplifies the solution process if we put the house as the column header. This is why house is the natural choice for the column header. I call the column header variable house as the primary variable to which values of all the other 5 variable values are to be ased. The empty logic table is shown below.
The job in hand is to fill up the 25 cells, or better still, find who owns the fish by analyzing the 15 logic statements. At first it seems we need to find all the five unique combinations of six variables filling up all 25 cells of the logic table. But on review of the problem, we perceive that we need just to find who owns the fish, even if some cells remain empty.
This is then our main objective. Additionally, in this improved solution, we will try to find the answer in as few steps and as quickly and simply as possible. This is our methodological objective. To achieve these objectives, throughout the solution process we will use powerful strategies, patterns and methods that are effective in solving these puzzles and are accumulated purely through solving many logic puzzles and Sudoku problems. These strategies and techniques are based upon common sense reasoning and I will explain the mechanism of each.
While solving this type of problem it is essential to form a strategy of processing the logic statements. Going serially from the first to the second and so on generally will end up into hopeless confusion.
The most important strategy at the start is to process those statements that make certain and definite asments to any of the cells. We call this strategy as the direct asment first strategy. Note: This makes sense at the start, as out of total uncertainty of all empty cells, a statement that states clearly with certainty that a variable value belongs to a single cell of the empty table must have the highest priority of processing.
In this problem, such a statement must have mention of a house by its position. As a specific national lives in a house at specific position and except color of the house, all the other three variables, Pet, Drinks and Smokes are actually attributes of the national, preference will be given to a statement in which a specific national is involved.
With these decisions, the "Statement 9. The Norwegian lives in the first house. This statement puts national Norwegian firmly in House 1 and accordingly the corresponding cell in the table is filled up. Any statement that refers to the already ased national and additionally helps to make another certain asment is chosen next. This asment by link or reference technique is extremely valuable and is used as soon as we get certain of a new value in the table. This is called link search technique. Accordingly, "Statement The Norwegian lives next to the blue house.
This is so because there is no house on the left of Norwegian's first house. It is use of elementary logic analysis which forms one of the main foundations of logic puzzle solving. When we get "blue" as the color of second house, we search for any statement that refers to "blue" and gives us another certain asment.
This method we follow as part of link search technique. In this case though we don't have such a statement. Link search chain , as I call it, ends here. But what about direct asment statements? Is there any more left? This is what I call repeating direct asment first and link search strategy. It is a combination of the two with repeating element and produces maximum certain asments quickly in this first stage.
Searching for the second direct asment, we locate "Statement 8. The man living in the center house drinks milk. With no further reference to already ased values "Norwegian", "milk" or "blue" and no more direct asment statements available, we have to adopt a new strategy based on a new pattern that we call temporary bonded member structure. Such structures can be formed on same variable values or values of different variables. Preference is for the first type of temporary bonded member structure on same variable values.
When a logic statement refers to two or more than two values of same variable , and mentions positional relation of the values column-wise , we get what we call, a temporary bonded member structure on same variable. Mark that the related values in a temporary bonded member structure of this type must be of same variable, and in this case must belong to the same row. If there is more than one such statement forming temporary bonded member structures, the statement that spans largest of bonded cells of a row is selected to be of highest potential. In our problem we identify "Statement 4.
The green house is on the left of the white house. This is the positional relation. By elementary logic analysis we can easily conclude that colors green on the left of white can only be ased to House 3-House 4 or House 4-House 5, as the first two houses are already blocked. We call this situation of only two possibilities as two degree uncertainty that is considered as partially certain and preferable. We can write down these two partially certain possibilities easily in the logic table. Because of only two possibilities, this has a high probability of a later statement removing one possibility by conflict and convert the remaining one as certain.
Certainty is the main goal we strive for. Thus by Statement 4, we get a temporary bonded member structure on same variable with two degree uncertainty. The following state of logic table will show how we record this temporary bonded member structure. With limited possibilities of green and white, now we search for a statement following our dependable link search technique , that refers to either green or white as well as creates new certain asments. Such a statement we find in "Statement 5. The green house's owner drinks coffee.
Color white automatically is ased to House 5. At one go we have three certain asments. Here we have used first link search technique on the values of temporary bonded member structure green-white and then principle of conflict to achieve multiple certain asment. Now perhaps you can realize the potential of creating and using a temporary bonded member structure.
A little further on we will use another advanced form of temporary bonded member structure to break a bottleneck. We could have processed the 4th and 5th statements together, but for showing the mechanism of the combined strategy we have separated out the two steps. We applied the earlier strategies during the initial stages when the logic table was nearly empty. But as the logic table now is fairly filled up and also the patterns used in the earlier strategies are no longer available, we look for new and easier opportunities. By this strategy, basically we look for conflicts resulting in certain asments.
It makes sense that,. A row or column that is filled up with maximum of cell values, or having minimum of empty cells will have the highest potential for a statement creating a certain asment. The target row at this stage is the row of house color, and as expected, the "Statement 1. The Brit lives in the red house. The elementary logic analysis is straightforward.Einstein riddle fish
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