Classic riddles

The Einstein riddle, solved step by step

The 15 clues, the complete solution and — the part that almost never gets explained — why you do not need to guess at any point.

Legend has it that Einstein wrote this riddle as a boy and claimed that only 2% of the population could solve it. There is no evidence that it is his, or that he ever said such a thing, and that 2% is an invented figure that has been repeated for decades. What is true is that it has become the textbook example of the logic grid puzzle, and that it can be solved entirely by reasoning.

Here is the statement, and then the full solution. If you want to try it yourself, this is the moment to stop.

The statement

There are five houses in a row, each a different colour. In each house lives a person of a different nationality. Each of them drinks one beverage, smokes one brand and keeps one pet, all different from each other.

The question is: who owns the fish?

1. The Brit lives in the red house.
2. The Swede keeps a dog.
3. The Dane drinks tea.
4. The green house is immediately to the left of the white one.
5. The green house owner drinks coffee.
6. The person who smokes Pall Mall raises birds.
7. The owner of the yellow house smokes Dunhill.
8. The person living in the centre house drinks milk.
9. The Norwegian lives in the first house.
10. The person who smokes Blends lives next to the one who keeps a cat.
11. The person who keeps a horse lives next to the one who smokes Dunhill.
12. The person who smokes Bluemasters drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The person who smokes Blends has a neighbour who drinks water.

The method: start with what is beyond dispute

The most common mistake is to read all fifteen clues in a row and feel overwhelmed. You do not need to understand them all at once. The technique is to find the clues that pin something down absolutely first, place them, and then re-read the rest with that new information on the table. Clues that said nothing before suddenly say a great deal.

Step 1: the three certainties

Three clues depend on nothing else:

• The Norwegian is in house 1 (clue 9).
• Whoever lives in house 3 drinks milk (clue 8).
• House 2 is blue: clue 14 says the Norwegian lives next to the blue house, and since the Norwegian is in the first, his only neighbour is the second.

Step 2: the green-white block

Clue 4 says the green house is immediately to the left of the white one. That pair can only occupy positions 1-2, 2-3, 3-4 or 4-5. The first two fall away because house 2 is already blue. And the 3-4 pair falls too, because the green house drinks coffee (clue 5) and house 3 drinks milk.

Only one option remains: house 4 green, house 5 white. And by elimination, since the Brit is in the red house (clue 1) and the Norwegian in house 1 cannot be the Brit, house 1 is yellow and house 3 is red, with the Brit inside it.

Notice what just happened: clue 4, which on its own said practically nothing, resolved all five colours the moment it was combined with what we already knew.

Step 3: the drinks and the first brands

The green house (number 4) drinks coffee. Number 3 drinks milk. Clue 7 tells us the owner of the yellow house — number 1 — smokes Dunhill, and clue 11 that the horse keeper lives next to him: the horse is in house 2.

The Dane drinks tea (clue 3). He cannot be the Norwegian in house 1, nor the occupants of 3 and 4, who already have drinks: he is in 2 or in 5.

Suppose he were in 5. Tea would then belong to house 5, and houses 1 and 2 would be left with water and beer. House 1 smokes Dunhill, so it does not smoke Bluemasters; and since the Bluemasters smoker drinks beer (clue 12), house 1 does not drink beer either. It would take the water, and house 2 the beer along with Bluemasters. But clue 15 says the Blends smoker has a neighbour who drinks water, and the only neighbour of house 1 is house 2 — which we have just assigned to Bluemasters. Contradiction.

Therefore the Dane is in house 2 and drinks tea, which leaves the water for house 1 and the beer for house 5. And since the Bluemasters smoker drinks beer, house 5 smokes Bluemasters.

Step 4: nationalities and the fish

The Swede keeps a dog (clue 2) and the German smokes Prince (clue 13). Of houses 4 and 5, number 5 already smokes Bluemasters, so the German cannot be there: the German is in house 4 and the Swede in house 5, with his dog.

That leaves Pall Mall and Blends for houses 2 and 3. Clue 6 says the Pall Mall smoker raises birds, and clue 15 that the Blends smoker has a neighbour who drinks water — the water is in house 1, so Blends is house 2 and Pall Mall house 3, with the birds.

Clue 10 finishes it off: the Blends smoker (house 2) lives next to the cat owner. His neighbours are 1 and 3; house 3 already has birds, so the cat is in house 1.

And only one house is left without a pet.

The solution

The German owns the fish.

What this riddle actually teaches

Beyond the answer, there are three ideas here that apply to any puzzle of this kind.

Negative clues are worth as much as positive ones

"The Dane drinks tea" looks more useful than "the green house is to the left of the white one". But it was the second that resolved the colours. Clues that only eliminate possibilities do not hand you a direct answer, which is why they get ignored; yet they are the ones that narrow the ground so that the positive clues become decisive.

The reading order is not the usage order

The clues are numbered, but that order is arbitrary. Solving consists of going round them again and again asking "with what I now know, does this clue say something yet?". A clue that is useless on the first lap can be the key on the fourth.

If you find yourself guessing, you missed a deduction

In a well-built puzzle you never need to assume anything. When you catch yourself thinking "let me try putting the fish here and see if it breaks", it almost always means there is a clue that still has something to say and you have not gone back to it. It is worth re-reading before taking the hypothesis shortcut: the shortcut works, but it robs you of the good part.