The Einstein Puzzle Solution

From StoneHome

In order to solve an Einstein Puzzle, first sort out all the concrete information you've been given. Then, induce whatever you can from correlary relationships, and use complete sets where available to deduce remainders. If the puzzle is well made, you should be able to deduce the entire set of information through these maneuvers, with the last piece of information falling into place as the solution.

Methodology

This puzzle is easiest if it's gridded. Gridding it means choosing axes. The Y Axis should be the axes of data, of which there are six: name, color, drink, smoke, pet, and the one people tend to forget, office number. Though any of the data are legal, the two sensible choices for X are office number and name. I use office number, though name leads to a very different solution path which is also fun. (More complex variations of this game require you to visualize this table in multiple ways, by introducing other orderings to the set than just the office number, or by introducing partial orderings; this one you can get by on with a single 2d table.)

Initial Data

If your axis is office position, then two pieces of hard knowledge are introduced at the beginning of the game:

• David is in office 1
• Center office drinks milk

From those two pieces of information, we can create the following grid:

Deduction and Induction

Next, we fill the grid in by induction.

• Because of rule 14 (David's office is next door to the office with a blue door,) and because we know Davis is in #1, the only possible neighbor is Office 2. Therefore, Office 2 has a blue door.
• Next, because of rule 4 (The green office door is to the left of the white office door,) we can eliminate doors 1 and 2 (1 can't have white to its right, 2 is occupied) as well as door 5 (5 can't have anything to the right.) Therefore, the green door must be either #3 or #4. Because rule 5 says Green drinks coffee, and since we know #3 is milk, the green door must be #4, and therefore the white door is #5.
• By rule 5, we can now assign coffee to #4, since we know where green is.
• By rule 1, we know that Alvin has a red door. Since only two colors remain, #1 and #3, and since we know Alvin isn't in #1, then Alvin must be in #3, meaning #3 is the red door.
• Therefore, since all other colors are solved, #1 must be the yellow door.
• By rule 7, we know that the yellow door smokes El Cigar

This gives us the following updated chart:

• By rule 11, we know that the horse lover is next door to the smoker of El Cigar, which makes the horse lover door #2.
• Through rule 3, we know that Bill drinks tea. Only #2 and #5 have both the name and drink slot open.
• Via rule 12, we know that beer and cigarettes go together. Only #2 and #5 have the drink and smoke slot open.
• If Bill was in #5, then beer/cigarettes would have to be #2. That would leave slot #1 as the only place for water. However, we know that water and the non-smoker are neighbors, and this arrangement would leave cigarettes as water's only neighbor. Therefore, Bill cannot be #5. This means Bill is #2, that #2 drinks tea, and therefore through rule 12, we also know #5 must be beer and cigarettes.
• Water still only fits in one slot, slot #1. Through rule 15 we know water's neighbor is a non-smoker, which means #2 is a non-smoker.

This gives us the following updated chart:

• By rule 13, we know that Chuck smokes a pipe. This can only fit in slot #4.
• This means only the Oral Pouch is left for tobacco, which must be slot #3.
• This also means only Edward is left to fill slot #5.
• By rule 6, we know the person with the oral pouch (Alvin) keeps birds.
• By rule 2, we know Edward keeps dogs.
• By rule 10, we know that the non-smoker has a cat next door; since #3 is filled, this must be #1.

This gives us the following completed chart:

Answer

The only slot remaining to be filled is Chuck in #4, who must have a fish for a pet.