## Hassan’s Horses

Last month I gave my students a problem from Raymond Smullyan’s book The Riddle of Scheherazade:

A certain sheik named Hassan has eight horses. Four of them are white, three are black, and one is brown. How many of them can each say that it is the same color as another one of Hassan’s horses?

Half of my students failed to notice the trick and gave the wrong answer. Recently I gave them the continuation of the problem from the same book:

A certain sheik named Hassan has eight horses. Four of them are white, three are black, and one is brown. Assuming now that Hassan’s horses can talk, how many of them can each say that it is the same color as another one of Hassan’s horses?

This time the majority of my students didn’t notice the trick. This motivated me to continue playing jokes with them. Unfortunately though, Raymond Smullyan had only two problems about Hassan’s horses, so I have to invent the next one myself. Here is what I plan to give my students next time:

A certain sheik named Hassan has eight horses. Four of them are white, three are black, and one is brown. Assuming now that Hassan’s horses can talk and always tell the truth, how many of them will say that it is the same color as another one of Hassan’s horses?

Feel free to continue the series.

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1. #### Jason:

I thought you didn’t like ambiguous and/or culturally-specific puzzles? The answer to the first puzzle is either 7 or 0 depending on the meaning of “can each say”. The literal meaning refers to whether or not the horses can speak, giving an answer of zero. The idiomatic meaning refers to whether or not the statement is true, giving an answer of 7.

2. #### Konstantin:

A certain sheik named Hassan has eight horses. Four of them are white, three are black, and one is brown. Assuming now that Hassan’s horses can talk and always tell the truth and no one of them is daltonian, how many of them will say that it is the same color as another one of Hassan’s horses?

3. #### Andy:

Well perhaps horses can “say” things without using human language, so its hard to argue that the answer to the first problem is ever “0”, unless you are being intentionally obtuse.

4. #### Andrew MW:

Also, they must not be blind.

Also, their visual cortex must work.

Also, they must know what colour the other horses are (they could be in 8 different fields scattered across the middle east!).

Andy, this seems to be an exercise in being intentionally obtuse! (or at least uncovering as many hidden assumptions as possible!)

5. #### colorblind:

“Assuming now that Hassan’s horses can talk and always tell the truth, how many of them will say that it is the same color as another one of Hassan’s horses?”

You’ve changed the question from “can” to “will”. I’m not sure how often the question of color comes up in horse conversation, so I can’t answer the question definitively anymore. Now if they’re prompted to answer…

6. #### Blaine:

* must be able to determine color
* must be able to think logically like students 🙂
* must be able to speak in a language understandable to the listener
* must be able to see the color of every other horse
* blah, blah, blah

7. #### Bill:

Now that’s a horse of a different color! Being intentionally obtuse is somewhat of a specialty of mine. Sometimes I don’t even know I’m doing it!

Does “another one” mean exactly one? Or could a possible response be “I am not the same color as another ONE of Hassan’s horses, but rather three of Hassan’s horses.” Similarly, the problem does not state that Hassan has ONLY eight horses.

Does a horse have to be owned by the same “Hassan” to be called “one of Hassan’s horses” in this scenario?

The problem says that Hassan “has” the horses, but not that he owns them. He may have someone else’s horses in his possession for a variety of reasons. Therefore, none of the eight horses are “Hassan’s horses” necessarily.

The word “white” conversationally can refer to a range of different specific colors. So if one of the horses is cream and another is ivory, they may both be white without being the same color.