### Brain Teasers

# 9 Dishes on the Menu

A particular inn always offers the same nine dishes on its dinner menu: A, B, C, D, E, F, G, H and I. Five foreigners arrive. Nobody tells them which dish corresponds to each letter and so they each select one letter without knowing what they will eat. The innkeeper arrives with the five dishes ordered and puts them in the center of the table so that they can decide who eats what. This goes on for two more nights. The foreigners, who are professors of logic, were able to deduce by the dishes they ordered which letter represents what dish. What could have been the dishes ordered each of the three nights? Note: Each dish was ordered at least once.

### Answer

They could have ordered ABCDD their first night (finding out what D is), AEFGG the second night (finding out what G is and what A is, since they had ordered it the previous night too), and BEHII the third night (finding out what I, B and E are). This leaves C, F and H out, and since they had never ordered these dishes twice, and each came out on a different night, they should know what they are.Hide Answer Show Answer

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## Comments

I got it a different way:

Night 1 :A, B, C, C, D

(duplicate dish is C)

Night 2: A, F, D, D, E

(duplicate dish is D, dish same as previous night is A, dish missing from previous night is B)

Night 3: E, G, G, H, B

(duplicate dish is G, dish same as previous night is E, dish H is new dish, dish I is the dish never ordered)

Night 1 :A, B, C, C, D

(duplicate dish is C)

Night 2: A, F, D, D, E

(duplicate dish is D, dish same as previous night is A, dish missing from previous night is B)

Night 3: E, G, G, H, B

(duplicate dish is G, dish same as previous night is E, dish H is new dish, dish I is the dish never ordered)

The very last sentence of the puzzle states "Each dish was ordered atleast once". In your solution, you say that dish I was never ordered. Hence, your solution is incorrect. However, if that last sentence was omitted from the puzzle, your solution would have also been correct.

One of the best. Straight to my favourites.

Good one!

i think your comment is wrong vivec

great logic teaser!!

How would they know which dish was "B" and which dish was "E"? They would know which two dishes to narrow them down to, but not which was which.

Outstanding! The solution algorithm somehow reminded me of the technique used in playing Mastermind... but don't ask me to quantify that.

...

seanlandrews - They distinguish E & B by remembering which dish they'd seen the first night (B) and which they'd seen the second night (E).

...

seanlandrews - They distinguish E & B by remembering which dish they'd seen the first night (B) and which they'd seen the second night (E).

I got it a different way too! I did it as follows:

AABCD (they will find out which A is)

DEEFG (they will then find out D and E)

HHIBF (they will find out H, I, B and F)

Through elimination as they now know A, B and D, they will know C as well. Through elimination the same way, they will also know the identity of G as they now know the identities of D, E, and F.

Awesome puzzle, very fun and so happy to figure it out!!

AABCD (they will find out which A is)

DEEFG (they will then find out D and E)

HHIBF (they will find out H, I, B and F)

Through elimination as they now know A, B and D, they will know C as well. Through elimination the same way, they will also know the identity of G as they now know the identities of D, E, and F.

Awesome puzzle, very fun and so happy to figure it out!!

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