A teacher writes six words on a board:
CAT DOG HAS MAX DIM TAG
She gives three students Abner, Bentley, and Charlotte each a piece of paper with precisely one letter from one of the words, so that:
- Each student gets a different letter, and:
- All three students get a letter from the same word.
Then she asks, "Abner, do you know the word?"
Abner immediately replies "yes".
She then asks, "Bentley, do you know the word?"
Bentley thinks for a moment and replies "yes".
Then she asks Charlotte the same question.
Charlotte thinks for a short while and then replies "yes".
What is the word?
To help make a consensus and alleviate my own confusion - did I remember correctly the first time? - I redid my work:
1) Abner must have one of C,H,I,O,S, or X to know.
That also eliminates TAG. All five other words are possible.
2) Bentley can not have any of those letters. Also, he cannot have A,D, or M, or else he would still not know, since each allows two possibilities. So Bentley has G or T. So, the only words that are possibly correct are CAT and DOG. Thus, Abner must have C or O.
3) Charlotte, after thinking, would know it is CAT or DOG. Also, she must have an A or D. So, yes - Charlotte would know the answer. But the answer could be CAT or DOG (She must think through step 2, or else her A or D would yield multiple answers: (CAT, HAS, MAX) (DOG, DIM) )
So I get either CAT or DOG .
reigning cats and dogs
