How to Answer Einstein's Logic Problem, "Who Keeps Fish?"
Logic puzzles are typically viewed with an initial look of dread, their many variables and heavy wording casting a doubtful shadow over the possibility of a simple solution. When you add in the fact that one of the most famous logic puzzles around was reportedly invented by Albert Einstein as far back as the 19th century, you may already be considering waving the white flag before you even embark on the long and winding journey. Additionally, the legend also states that Einstein estimated that 98% of the world's population would never be able to solve his puzzle, which adds yet another layer of intimidation to this menacing, headache-inducing problem. Even though our pursuit to solve Einstein's famous puzzle might prove to be ultimately futile, let's take up the challenge anyway to see if we can construct a logical path that will lead us to his elusive solution.
Einstein's Problem: The Facts
Einstein's logic problem consists of three parts: a list of facts, a simple question and a list of clues to help us along. Einstein assures us that the facts and clues he provides can be used together in order to answer the question he poses, although he does not say how they will interact. The first step in solving this mystery will be to review each of these three components, which are presented below.
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Einstein's List of Facts 1. There are 5 houses (in a row) painted 5 different colors: Blue, Green, Red, White and Yellow. |
So now we have a somewhat cryptic list of facts about FIVE different owners, each of whom live in one of FIVE different houses. Each of these owners apparently has a favorite drink, and even a favorite cigar. They each also raise a certain type of pet. The last line in the fact list also tells us that none of the owners share any of their favorites, pets or houses with another owner. In other words, each attribute (the color of their house, their nationality, favorite drink or cigar and even their pet) is unique to only one owner. For example, if one owner's favorite cigar is Bluemaster, then no other owner would have that certain brand as a favorite. OK, but what does this list of facts have to do with anything? Well, it must now be time for the famous question.
Einstein's Question: "Who Keeps Fish?"
Using the facts above as a stepping stone, Einstein now poses a question. The seemingly simple query has Einstein wondering, "Who Keeps the Fish?". While we know that one of the five owners raises Fish, we certainly have no idea on how to figure out which specific owner it is yet. But what we do have is a fairly large list of attributes that we know are unique to their respective owners. So, in theory, if we can start to narrow down some of the possibilities as to which attributes match up with each owner, perhaps we would be able to gain a clearer picture of which owner could possibly raise the Fish. To do so, we'd have to successfully eliminate all of the other four possibilities (Cats, Birds, Dogs and Horses) for this mystery owner in order to be certain though. At this point Einstein offers up a sadistically innocent-looking list of 15 clues that will help us do just that.
Einstein's Puzzle: The Clues
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Einstein's List of Clues 1. The Brit lives in a Red house. |
Browsing through the list, we discover that Einstein's clues come in several varieties and should indeed help us start to gain a clearer picture as to who owns/likes/keeps what. It appears there are quite a few informational types of clues that simply state a concrete fact, connecting two of the variables together directly. For example, Clue #1 states that the Brit lives specifically in the Red House. While we don't know which house (out of the five) is Red, we at least know the nationality of the owner who lives there. We'll call these "Concrete Connecting Facts" since they specifically link two of the variables together without needing any further inspection. Actually, we can notice that almost all of the clues fall into this category with only a few exceptions. The Clues 1, 2, 3, 5, 6, 7, 8, 9, 12 and 13 are all factual based, while the remaining clues (4, 10, 11, 14 and 15) are a bit more complex. We'll call this group of clues "Relative Location Facts" since their locations are relative to other variables which still need to be solved before they'll be of any use to us. For example, Clue #4 states that the Green house is on the left of the White house. To use this clue, we'll first have to figure out where the White house is located. Before we initiate our investigation, though, let's refresh our list to reflect the classifications we just created.
Simplifying The Clues List
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Concrete Connecting Facts 1. The Brit lives in a Red house. (Brit + Red) Relative Location Facts 4. The Green house is on the left of the White house. |
In the expanded and optimized list of clues to the right, we've added several abbreviated versions of each clue in parentheses. These short-hand versions show each of the pertinent variables for each clue joined together, and help us focus on their relationship to the remainder of the clues.
For example, Clue #1 now shows (Brit + Red) beside the full clue description. It is condensed in this way because we know that both the owner who is British (one of the five nationality variables) and the Red house (house color variable) are joined together based on the clues list. The remainder of the clues are broken down in this manner for the Concrete clues. Underneath each of the Relative clues we can see that there are also somewhat larger descriptions that attempt to simplify each clue. We now have a solid base of puzzle pieces to work with as we try to "find the corners" and work our way towards a comprehensive solution. It's now time to solve this enigma in a step-by-step fashion using only the information we've covered to this point.
SPOILER WARNING! Please Read Before You Continue
Let's pause here momentarily and express the importance of attempting to solve Einstein's Puzzle yourself before you go through our solution, which WILL reveal the answer near the end of the guide. The fun-factor with logic puzzles such as this comes from working through them yourself and trying to find your way around the many winding corners. But if you skip ahead and look at the answer, remember that you can never go back to trying to solve it on your own. So before you read any further WE STRONGLY URGE YOU TO STOP HERE AND TRY TO SOLVE IT YOURSELF! See if you can answer Einstein's question and discover who raises Fish. If you can resist the urge to look now, you can be sure that you will be much more satisfied with yourself if you can solve it on your own. However, if you've already attempted the solution and feel that you are inexorably stuck (or are just the curious type that wants to know the ending to the book without actually reading it) let's continue down the page where we'll break down each of the variables and put this famous puzzle to rest!
The Norwegian
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House Location Specific Clues 9. Norwegian + first house. What did we figure out? Since there are 5 houses in a row, 1-2-3-4-5, |
We'll employ a good puzzle-solving technique to get us started off in the right direction, which involves searching for clues that occur two or more times in the list. Finding these multi-purpose types of variables, those that are used or mentioned several times thereby increasing their importance, will help us solve larger chunks of information simply because they have a broader scope than clues that appear only once. Taking a quick inventory, one of the first variables we notice is the Norwegian owner. The Norwegian is not only listed in two separate clues, but one is listed in the Concrete section and the other is listed in the Relative section. That means we'll already have a start on one of the more difficult relative types of clues and we'll have a factual clue to back up our analysis.
Clue #9 tells us the the Norwegian lives in the first house, so the first order of business is figuring out which house that is. To illustrate how to do so, let's remember the first line in Einstein's list of facts: There are 5 houses (in a row) painted 5 different colors: Blue, Green, Red, White and Yellow. Notice the emphasis we've added. Since we know there are five houses in a row, we can think of them in a sequence such as 1-2-3-4-5. We can further note that since the Norwegian must live in the first house, what we're really saying is that he must live in House #1 since it is the first house in the sequence.
Building on this information, we can now look at Clue #14 which states that the Norwegian must live (directly) next to the Blue house. Since we now know that the Norwegian lives in House #1 we can confidently surmise that House #2 must be Blue, simply because House #2 is the only house that can be directly beside House #1 (it's the next house number in the sequence). We now have a few solved variables, and they have been summarized in the helpful chart above. However, we still don't know very much about any of the other variables involved with either of these houses. It's time to remedy that.
House Colors, Locations and Drinks
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Using More Location Specific Clues 4. Green = left of White. What did we figure out? Since there are 5 houses in a row, 1-2-3-4-5, Also, that House #3 drinks Milk. Anything else? Since Green must be left of White, Since the owner of the Green house drinks Coffee, House #4 must be Green and House #5 is White. And of course, The owner of House #4 drinks Coffee. |
Time to search the list for more variables that occur multiple times, and we inevitably find that the Green house fits the bill quite nicely. References to the Green house once again are found in both the Concrete list and Relative list, so we can assume they should be very helpful for our task. The first case we'll look at is Clue #4 which says that the Green house must be to the left of the White house. Considering we haven't figured out which house is Green yet, or White for that matter, it doesn't seem like this clue can be of much help to us. We only know one house color for sure so far, Blue House #2 from the analysis in the previous section, leaving us with the other four houses (1-3-4-5) to contend with. However, even though we can't use this relative clue to solve the location of either the Green or White house we can actually use it to narrow down our options by using some advanced reasoning.
Let's look at what Clue #4 again: The Green house must be to the left of the White house. Now let's put that together with the house color information (House #2 is Blue) we've solved already. What does this tell us? Most notably that House #1 CANNOT be Green. Why is that? Since we know that House #2 is blue, House #1 is the only house to the left of it in the housing sequence. Since House #2 isn't White, then House #1 can't be Green (Green must be left of White). Based on this, we can know confidently restrict the possible choices for either Green or White to Houses #3, #4 or #5.
Back to searching the clues for more house information. One item of interest is Clue #8 which says that the owner living in the center house drinks Milk. Well, since we know that all of the houses are in a row (1-2-3-4-5) we can realize that the center of the row sequence (House #3) must be the Milk drinker. But how does that help us? The second reference to the Green house, Clue #5 further tells us that the Green house owner drinks only Coffee. While this might make that owner very twitchy, we can at least deduce that he does not drink Milk. That means that the Green house cannot be House #3 since they drink Milk. We can therefore eliminate House #3 from the possibilities as well. That leaves us with either House #4 or #5 for our Green and White locations. And since we've already read that the Green house must be to the left of the White, we can actually see that House #4 must be Green and House #5 must be White!
Let's take a quick recap. So far we've solved several important variables: The Norwegian lives in House #1, House #2 is Blue, the owner of House #3 drinks Milk, House #4 is Green, House #5 is White and the owner of House #4 drinks Coffee. Whew! That's a pretty good result from only looking at a total of five clues. Since we've already solved three out of the five house colors, the next logical step will be to solve the remaining two. We have two colors left (Red and Yellow) and two locations (#1 and #3) to contend with.
The Brit
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The Brit's Clue 1. Brit + Red. What did we figure out? House #3 is Red. |
We know that House #1 belongs to the Norwegian, but we can't figure out which color his house is just yet. However, we'll once again search Einstein's list of clues to see if we can find any more information. Lo and behold we come across concrete factual Clue #1: The Brit lives in the Red house. Using the same methods as above, we can eliminate one of our options based on only this information. Since we know the Brit must live in the Red house, we can determine that he CANNOT live in the Yellow house. That means the Norwegian must live in the Yellow house. And if the Norwegians house (House #1) is Yellow, that means House #3 must be Red and belong to the Brit! We now have all the House colors solved, and can even place two nationalities inside of them. As usual, since we have discovered more information we will now search through our clues list once again to continue our solution.
The Dunhill Connection
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The Two Dunhill Clues 7. Yellow + Dunhill. What did we figure out? House #1 (Norwegian) smokes Dunhill. |
Clue #7 contains a reference to the Yellow house, stating that the Yellow house owner smokes the Dunhill brand of cigars. Since we just figured out that the Norwegian owns Yellow House #1 we understand that he must be the fellow that smokes Dunhill cigars. And now that we know where the Dunhill smoker lives, we can use Clue #11 to our advantage. It says that the owner who keeps horses lives next to the man who smokes Dunhills. Logically, the only house that can be beside House #1 is House #2, so the owner of Blue House #2 must be the one who raises Horses. Whoa! That means we can already eliminate the owner of House #2, whomever that turns out to be, as the owner that raises Fish! Remember, discovering which owner raises fish is the main goal of our puzzle so we've obviously just taken a very good step in the right direction. This looks like a great time to pause and reflect on what we've learned to date.
Examining the Seven Remaining Clues
| 1 | 2 | 3 | 4 | 5 | |
| Color | Yellow | Blue | Red | Green | White |
| Nationality | Norwegian | ??? | Brit | ??? | ??? |
| Drink | ??? | ??? | Milk | Coffee | ??? |
| Pet | ??? | Horses | ??? | ??? | ??? |
| Cigar | Dunhill | ??? | ??? | ??? | ??? |
In the chart to the right, we've listed a summary of the variables solved so far. The five main variables (House Color, Nationality, Drink, Pet and Cigar) are cross-referenced with each corresponding house location (#1 through #5) and the solutions found for each house are listed in the appropriate column. Looking at the chart we can see that while we've made great strides in figuring out a solution, there are still lots of question marks in each column meaning we still have our work cut out for us. However, using this chart will help us in our next couple of steps since it provides a visual point of reference as to which variables we need to solve for each house. Take a moment to review each entry and scroll back up the page in order to check the work if you need further reinforcement of how we arrived at the information contained here. We'll now use this handy chart to dissect the few remaining clues.
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The Remaining Factual Clues 2. Swede + Dogs (House #4 or #5) The Remaining Relative Clues 10. Blend must neighbor Cats. Under these terms, there are four options: Blend in House #2 with Cats and Water BOTH in #1. |
We've successfully used 8 out of the 15 total clues Einstein had provided for us, and from those eight clues we've gleaned a whopping 11 variables out of the 25 total variables listed at the start of the puzzle. We're now left with only 7 remaining clues, with five "factual" types and only two "relative" types. We'll use the table above as a helpful reference to see where each of the remaining combinations of attributes can potentially be placed. For example, Clue #2 tells us that the Swede raises Dogs (and therefore not Fish). However, we don't know which house the Swede lives in yet, only that he raises Dogs. Using the summary chart, though, we can examine which houses the Swede/Dog combination can, and cannot, actually exist.
Moving across the chart from the left, we recall that the Norwegian lives in House #1. We can therefore eliminate it from the potential homes for the Swede/Dog combination. And since we know that the mystery owner of House #2 raises Horses, we can also eliminate it from the list of potentials. House #3 can also come off the list too since we already know the Brit lives there. That only leaves us with Houses #4 and #5 as possibilities for the Swede who raises Dogs. Using the same logic, we can work out the remaining clues and their subsequent options, all of which are listed in parentheses next to each clue. This is all true, of course, because we know that none of the owners may live in the same house or share any attributes. The two remaining "relative" clues may also be examined in this way. Clue #10 says the owner who smokes Blend Cigars must live directly next to the owner who raises Cats. Clue #15 also concerns the Blend brand and says that the owner who smokes them must also live directly beside the owner who drinks Water. Based on this information, there are only four different options for this scenario to occur, and they are also listed in the chart below the two clues.
Plugging In Our Available Options
| 1 | 2 | 3 | 4 | 5 | |
| Color | Yellow | Blue | Red | Green | White |
| Nationality | Norwegian | Dane | Brit | ??? | ??? |
| Drink | ??? | Tea | Milk | Coffee | Beer |
| Pet | ??? | Horses | ??? | ??? | ??? |
| Cigars | Dunhill | ??? | ??? | ??? | Bluemaster |
Now let's take a closer look at the results of the last step. Notice that two of the clues, Clue #3 and Clue #12, share a few similarities. Most notably, each combination has a Drink in it AND they both share the same house-location possibilities (House #2 or #5). We have found an either-or situation! What this means is that if the Dane/Tea combination can be proven to go into one location, then the Beer/Bluemaster combination must belong in the other. Since we have no way of knowing which one goes where yet, we'll simply try plugging in the combinations one at a time to see which one works. First we'll try the Dane/Tea Combination in House #2 and the Beer/Bluemaster combo in House #5. They are listed in bold above.
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Blend in House #2 with Cats and Water BOTH in #1. |
Now we'll see if we can make any of the relative clues work with this combination. If we can't, then we'll know that the opposite configuration would be correct. To do so, we'll have to check if we can still input any of the relative options into the new chart. The first option (Blend in House #3 with Cats/Water BOTH in #1) is still a possibility. The second option (Blend in House #3 with Cats in #4 and Water in #2) needs to be examined. We find out that in the new chart this option is NOT available any longer. This is because it requires the owner of House #2 to drink Water, but the Dane only drinks Tea. It gets crossed off the list. The third option also gets axed, since it would require the owner of House #5 to drink Water. That mystery owner is obviously very manly and only drinks Beer. And looking at the fourth option, we see that it is also not possible due to the fact that once again it would require Cats and Water to both be located in House #5. As we just stated, the owner of House #5 quenches their thirst only with a frosty mug of Beer, period. So where does that leave us? Well it actually gives us only one option for placing the attributes found in the last two relative clues: Option 1, Blend in House #2 with Cats and Water BOTH in #1. Therefore, we know that the Dane/Tea and Beer/Bluemaster combinations must be correct. For posterity's sake we did try the other combination just to make sure and it didn't work, but feel free to verify it on your own!
Solution to Einstein's Problem
| 1 | 2 | 3 | 4 | 5 | |
| Color | Yellow | Blue | Red | Green | White |
| Nationality | Norwegian | Dane | Brit | ??? | ??? |
| Drinks | Water | Tea | Milk | Coffee | Beer |
| Pet | Cats | Horses | ??? | ??? | ??? |
| Cigar | Dunhill | Blend | ??? | ??? | Bluemaster |
We are now getting very close to a solution, with only seven variables left to solve. One of those variables will give us the solution to the entire puzzle: Who Keeps the Fish? After we plug in our last two solved variables from the previous step (listed in bold) it's time once again to examine the last three remaining clues to see where they can fit, and where they cannot. Our chart has become flush with answers so the amount of options has been reduced significantly. In fact, if we start with the German/Prince combo it looks like all of the remaining clues will now have only one option left, which means we should be able to see the finish line!
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Last Few Clues German + Prince (House #4). |
The only available option for the German/Prince combo is now House #4, since the owner of House #5 smokes Bluemaster and the Brit lives in House #3. And since that is the case, the only location that will work for the Pall/Bird combination would be in House #3. That only leaves one house left for the Swede and his Dogs, and we can confidently place them both into House #5. So who is it? Which one of the remaining owners raises Fish? All of our hard work has led us to the solution, which reveals the identity of the mystery owner and their elusive pet.
And the Owner Who Keeps Fish is...
| 1 | 2 | 3 | 4 | 5 | |
| Color | Yellow | Blue | Red | Green | White |
| Nationality | Norwegian | Dane | Brit | German | Swede |
| Drinks | Water | Tea | Milk | Coffee | Beer |
| Pet | Cats | Horses | Birds | FISH! | Dogs |
| Cigar | Dunhill | Blend | Pall Mall | Prince | Bluemaster |
As you can see in the chart to the right, we've come to our final conclusion: The German Keeps Fish! If you arrived at the correct solution in a different way than this congratulations are in order nonetheless, since there are in fact many different ways in which to solve this logic puzzle. Unless you took the 1 in 5 shot and threw out a random guess and got lucky without doing any of the work, well done! This guide may also be analyzed further to understand how a seemingly too-complex problem may be broken down into smaller, more manageable fragments which can be solved independently in order to tackle the bigger problem as a whole. I'm not sure about you, but I certainly enjoyed the process just as much as finally arriving at the solution to Einstein's famous problem!
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