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?
The first and last steps in my solution were pretty obvious but the middle part may need a little more explaining, so here goes:
Abner must have a letter that appears only once. Therefore he has one of C, H, I, O, S, X. This rules out the word TAG.
If Abner has C, the word is CAT and therefore Bentley has the A or T. Similarly, if Abner has H, Bentley has A or S. If Abner has I, Bentley has D or M. If Abner has O, Bentley has D or G. If Abner has S, Bentley has H or A. If Abner has X, Bentley has M or A.
So, naively, Bentley has one of A, T, A, S, D, M, D, G, H, A, M, A. But since Bentley knows the word, he must have a letter that appears only once in this list. This narrows it down to T, S, G, H. (This now rules out the words DIM and MAX, which rules out I and X as possibilities for Abner.)
Now if Abner has C, then Bentley has T, and Charlotte has A.
If Abner has H, then Bentley has S and Charlotte has A.
If Abner has S, then Bentley has H and Charlotte has A.
If Abner has O, then Bentley has G and Charlotte has D.
Since Charlotte knows the word, she must have D and the word is DOG.
Edited on April 10, 2022, 8:32 am
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Posted by tomarken
on 2022-04-10 06:21:57 |
Solution, explained further
