### Answer: Albert Einstein's hardest riddle

This is the answer to Albert Einstein's hardest riddle.

The best way to tackle the Albert Einstein riddle is systematically. To start with lay out what is known about each of the agents in a grid. In this case the agents are the men who are mentioned in the question. Each man has a number of attributes. These are: nationality; colour; drink; whether or not he smokes a cigar; and whether he has a pet. So, the grid will look like this:

Now in the puzzle it steps up a gear. Up to this point we've got away with adding single facts, but that strategy now leads to a dead end - the information that's left is too sparse. We need to start grouping assertions together to make progress.

The best way to tackle the Albert Einstein riddle is systematically. To start with lay out what is known about each of the agents in a grid. In this case the agents are the men who are mentioned in the question. Each man has a number of attributes. These are: nationality; colour; drink; whether or not he smokes a cigar; and whether he has a pet. So, the grid will look like this:

By laying this out as a grid we
can start to assign the attributes which are mentioned directly in the
question to some of the agents. As they are given to us we can simply
state these as assertions. So for example the man in the middle house
likes to drink milk. This is stated in clue number eight. This goes into
the grid as follows.

Having
written these down the next step is to start to deduce values for the
empty cells from question and clues. So for example question number nine
mentions that a Norwegian lives in the first house. There are two
possible positions for this house. The first being on the far left and
the second being on the far right. As there is no other information at
the moment it's largely arbitrary which one to choose - we can simply
choose one as our assumption. However given that this is our assumption
and not the question's we need to test it. If at any point it takes us
into an area which can't possibly be true we will have to reverse our
choice and try again.

So
let's assume the first house means the house on the extreme left.
Having made this assumption again we add it to the grid. Does this allow
us to progress on any of the other clues? As it turns out it does.
Number 14 says that the next house up from the Norwegian is blue. We can
then add this to the grid.

Again
iterating through the clues now we have this additional piece of
information we can see that more cells can be filled in. Clue number
four, for example, says that the greenhouse is to the left of the white.
Number five says it is occupied by a coffee drinker. The only place
that this could be is four so we can fill in both colour of the house
and a drink for the cell. We can also note white as the colour of the
fifth column.

This
is how to go through the rest of the riddle. Every time additional
information is added to the grid, go back over the cells with the
original clues to see if any now can be filled in. For example we can
now look at clue number one which says it's a Brit in the red house.
That's two pieces of information which are tied together. Previously we
didn't have anywhere to put this. However now there is only one
possible place so we can add it.

Now
we only have one house where the colour is still to be specified. It is
trivial then to deduce from the clue that this should be yellow.
Moreover we have in clue number seven that whoever is at the yellow
house smokes Dunhill, so we get that one as well now.

Now in the puzzle it steps up a gear. Up to this point we've got away with adding single facts, but that strategy now leads to a dead end - the information that's left is too sparse. We need to start grouping assertions together to make progress.

The
first of these is the man who both drinks beer and smokes Blue Master.
So we need to look for one option for nationality that could have
both. We know it's not the Norwegian - he smokes Dunhill. We also know
it's not the Brit - he drinks milk. Clue 13 states that the German
smokes Princes, so it can't be him either. Of the two remaining (Danish
and Swedish) clue 3 tells us that it's not the Dane - he drinks tea.
So it's got to be the Swedish guy.

Problem is, we could put this into two places - the 2nd column or the 5th - as both fit. We need to look for a clue which rules one out. Luckily, we have this in clue 2. This tells us that the Swede has dogs. So it can't be column two, because that already has horses for the pet.

Now as usually happens, it's all downhill to the end. Clue 15 puts the Blends smoker next to the water drinker. That can only go in column 2, with water going in column 1. That also gives us tea, for column 2. We know the tea drinker is Danish, so in it goes as well.

Problem is, we could put this into two places - the 2nd column or the 5th - as both fit. We need to look for a clue which rules one out. Luckily, we have this in clue 2. This tells us that the Swede has dogs. So it can't be column two, because that already has horses for the pet.

Now as usually happens, it's all downhill to the end. Clue 15 puts the Blends smoker next to the water drinker. That can only go in column 2, with water going in column 1. That also gives us tea, for column 2. We know the tea drinker is Danish, so in it goes as well.

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