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?
Because Abner knew the word immediately, he has one of C, H, I, O, S, X.
This rules out TAG.
Because Bentley knew the word, he has one of G, H, S, T.
This rules out MAX and DIM (and therefore means Abner has one of C, H, O, S).
If Abner has C, H, or S then Bentley has T, S, or H, respectively. In all three cases, Charlotte would have A and would therefore not know the word.
Since Charlotte did figure out the word, then Abner has O, Bentley has G, and Charlotte has D. The word is DOG.
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Posted by tomarken
on 2022-04-09 11:58:58 |
Solution
