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?
For A to know the word, he must have a letter that's uniquely represented amongst the possible words. These are: C, O, H, X, S, and I. So "TAG" is immediately eliminated.
From B's perspective, they know their own letter plus the fact that A was able to uniquely identify the word. If they had a D, for example, the word could be DOG (with A having O), or DIM (with A having I). In this way, DOG, DIM, and MAX can be eliminated. So the options now are either HAS or CAT.
For the word to be CAT, A would have had C, and B would have had T (since TAG was eliminated by A's statement). In this case C has the "A". From A's first statement C would know A has either a C, H, or S, while B has either T, S, or H, respectively. However, from the statements alone, I don't think there's a way for C to differentiate between these two scenarios.
The only thing I can think of is that A answers "immediately," while B "thinks for a moment." If the word was HAS, both A and B would be able to make the determination rapidly as both of them have unique letters. As B had to think for a moment, this suggests that the word is CAT.
Edit: On reflection, DOG would not be eliminated by B's statement. If B has a G, then A's first statement eliminates "TAG," allowing B to deduce that A has an O. In that case, C would have a D, and the options from her point of view are that A had either O or I, and B had either G or M.
Edited on April 9, 2022, 10:40 am
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Posted by H M
on 2022-04-09 10:34:30 |
Solution?
