How To Solve The Secret Word Logic Puzzle

A teacher writes six words on the board: cat, dog, has, max, dim, tag. The teacher hands a piece of paper to Albert, another to Bernard, and another to Cheryl. The teacher explains each paper contains a different letter from one of the words written on the board. The teacher asks if Albert knows the secret word, and *after a moment, he replies aloud, "Yes." The teacher then asks Bernard, and after a moment of thinking, he also says, "Yes." And finally Cheryl is asked and she takes a moment and then confidently replies, "Yes," she also knows the word. Albert, Bernard and Cheryl always ace their logic exams. What was the secret word? Watch the video for the solution.

*Since the original wording caused confusion, I meant to say each person takes a moment to think. As written in the video there was room for interpretation--if I were grading I would have accepted any logically reasoned conclusion.

My blog post for this video

I adapted this problem from the puzzle "Yes, Yes, Yes" in "The Great Book of Mind Teasers & Mind Puzzlers" by George J. Summers, which has the same situation with 5 words.

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[MindYourDecisions]

Welcome Mental Floss, Readers Digest, and MSN readers! This puzzle was recently featured in those sites and happy to have many new people learning about MindYourDecisions. As this puzzle is blowing up, I want to clarify one point:

As the original wording caused confusion, I meant to say each person takes a "moment" to think. I just used the "moment" as a way of saying each person thinks about his/her own letter and the other people's answers. In the video I only mentioned Bernard and Cheryl took a "moment, " so that caused confusion as to why Albert did not take a "moment." As written in the video there was room for interpretation--if I were grading I would have accepted any logically reasoned conclusion.

Links to articles:

[sairabarcelon]

Teacher: “Saira, do you know the word?” Saira, after a moment of thinking: “No”

[wolfval]

people struggling to find the solution, meanwhile am struggling to understand the damn question

[EpicFailureFive]

The problem with this solution is that Bernard's pause can be interpreted as him not having a unique letter, which would eliminate him having H and HAS as an option before Cheryl's turn. Which then opens the possibility of Cheryl having either A or D, leading to the answer being either CAT or DOG.

I believe you can fix this by adding HAT as a seventh word.

[mrsteve]

I was under the impression they had formed a new unique word from the letters they were given. :l

[jbohnoff]

Albert and Cheryl have been sleeping with each other and they've been communicating, non-verbally, during the exams. Meanwhile, Bernard was a former student of Hogwarts School of Witchcraft & Wizardry and an accomplished legilimens. Problem solved.

[LughSummerson]

Answer: Bernard cheats in his logic exams.

[-TheRF]

poorly written problem. Very confusing and allows a wide range of interpretations and answers (as we can see in the comments lol)

[Dragoonking]

I have a different solution:
Let's assume Albert got the letter "C". So he can be sure the word is "CAT".
Next Bernard got "T". But of cause he couldn't be sure about the word in the first place because there is also the word "TAG" But because "TAG" doesn't involve any unique letter, after Alberts statement he can be sure it has to be "CAT"
Last there's Cherly with her "A". She knows it can not be "TAG". It could be "HAS" but because Bernard had to think about the solution for a second, he needed Albert's help, so she can assume the word isn't "HAS" because there are two unique letters in it. It could only be "MAX" when Bernard got the letter "M" (because of the unique "X"), but in that case Bernard could not be sure about the word because "DIM" also involves his "M" and he couldn't say if Albert got the "I" from "DIM" or the "X" from "MAX". So she can also eliminate "MAX". That only leaves "CAT" for the solution.

That doesn't show "CAT" is the only correct answer but it proves that it is at least possible to be one of the correct answers.

[mauve]

I entirely misinterpreted the question and thought that only the unique letters between the words counted and I had to find what word could be spelled with those remaining letters.

So my answer was the word "six"

[giladporat]

I think "cat" can also be an answer if you consider the students high analytical skills as a clue. That is, Bernard could not have gotten any letter that appears only once because he needed to think briefly to identify the word (as opposed to Albert who immediately figured it out). So adding to the logic explained in the video, he couldn't have had "S" or "H"and Cheryl could therefore also eliminate the word "has". It leaves her with cat and dog, which she can deduce from knowing her own letter. Unfortunately we don't have this data and can't deduce the right word. Just a matter of perspective...

[Cogskate]

Badly worded puzzle. Two equally possible answers, because Bernard's pause eliminates "has".

[amylivingston]

Boy, was this question ever badly worded. I had no idea what "each paper contains a different letter from one of the words on the board" was supposed to mean. I initially thought it must mean "a letter that is not found in one of the words on the board, " and I couldn't figure out what they were supposed to guess from that. It would have been a lot clearer to say, "The teacher explains that each piece of paper contains one letter, and the three letters together spell out one of the words on the board."

Moreover, as TheQueue841 points out, the answer is wrong. The word could have been either "cat" or "dog, " because Cheryl had some additional information: she knew that Bernard had to think before saying he could identify the word. If his letter, like Albert's, had been a unique letter, he wouldn't have needed time to think. Thus, Cheryl would know the word couldn't be "has" - and thus she could have deduced "cat" from the letter A.

I give MindYourDecisions a D on this logic test.

[MRGCProductions]

the seccond letter couldnt have been H or S, since the problem explicitly says that bernard took a moment to think. Thus, his letter was not unique.

[tucker_d_dawg]

What if Bernards moment of thinking was NOT because he was considering Alberts answer, but rather because he was a slow reader and was carefully considering if his letter ("X" for example) actually uniquely identified the word? The fact they always ace their logic exams could be because they are thorough and double check their work. So the proposed solution of "Continuing from Alberts response" is actually a perhaps an erroneous ASSUMPTION about the reason Bernard paused,

[ayoubniyaz]

Based on the info provided, it could just as easily be "CAT" if Albert, Bernard and Cheryl got a C, T and A respectively.

HAS can be ruled out only because Bernard had to think a bit before identifying the word. But even that is an assumption

[saxbend]

it cannot be "has", because Bernard needed to hear Albert's response and have a moment of thinking before being able to determine whether he knew the word. Therefore cat and dog are equally likely. Cheryl can identify the word from her letter whichever it is, but to us as outsiders, we cannot distinguish between cat and dog without more information.

[vrndjn]

The answer could also be cat. This is because Cheryl knows that word couldn't be 'has'. This is because if Bernard had any of the letter 'h' or 's' he did not have to think to say yes.

[WhovianMinecrafter]

... or "cat"

Albert got the 'c', so he knows instantly.
Bernard got the 't' so once he knows it's not tag, then he knows for certain.
Cheryl has 'a' so she knows that it would not have taken both of the others a moment of thinking if it was 'has' and if Albert had 'x' for max then Bernard might have thought it could be 'dim', so Bernard wouldn't get it, therefor it would be 'cat'. There is no single answer for this.

[Jbrady]

There's definitely more than one way to interpret this.
First two both pick "has" because it is the only option with 2 unique letters.
Cheryl sees this to determine the word.