Which Alice?

Which Alice? Which Alice?

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ALICE IN PUZZLE-LAND THE NEXT TRIAL This problem is quite simple: Since A told the truth and accused one of the others, then B or C must be guilty. Therefore A is innocent. If everyone changed his accusation, but still accused someone else, B would have told the truth, and since we know that A is innocent, B would have accused C. Therefore C is guilty. THE NEXT TRIAL Since A told the truth, and he accused either B or C, then either B or C is guilty; so A is innocent. Now, the White Knight was either told that C lied or that C told the truth. If he had been told that C lied, he could not have known who was guilty, because it could be that C is guilty and falsely accused A (or for that matter B), or it could be that B is guilty and C falsely accused A. So, given that C lied, there is no way to determine whether B or C is guilty. On the other hand, given that C told the truth, he couldn't have accused A (who is innocent), so he accused B, and since he told the truth, B must be guilty. Therefore, the Jabberwocky must have told the White Knight that C told the truth, and the White Knight then knew that B must be guilty. ANOTHER CASE Again, since A told the truth and accused one of the others, he must be innocent. Now, if the White Knight had been told that C told the truth, then, without further information, he would have known that B was guilty (as we have seen in the solution of the last problem). But the White Knight could not, without further information, tell who was guilty; therefore, he must have been told that C lied. Then he was told whom C accused, and this enabled him to know who was guilty. If he had been told that C accused A, he couldn't have known whether B or C was guilty. So he must have been told that C accused B, which means that B must be innocent (since C lied), and since A is also innocent, C must be guilty. 176

ALICE IN PUZZLE-LAND<br />

THE NEXT TRIAL This problem is quite simple: Since A told<br />

the truth and accused one of the others, then B or C must be guilty.<br />

Therefore A is innocent. If everyone changed his accusation, but<br />

still accused someone else, B would have told the truth, and since we<br />

know that A is innocent, B would have accused C. Therefore C is<br />

guilty.<br />

THE NEXT TRIAL Since A told the truth, and he accused<br />

either B or C, then either B or C is guilty; so A is innocent.<br />

Now, the White Knight was either told that C lied or that C told<br />

the truth. If he had been told that C lied, he could not have known<br />

who was guilty, because it could be that C is guilty and falsely<br />

accused A (or for that matter B), or it could be that B is guilty and C<br />

falsely accused A. So, given that C lied, there is no way to determine<br />

whether B or C is guilty. On the other hand, given that C told the<br />

truth, he couldn't have accused A (who is innocent), so he accused<br />

B, and since he told the truth, B must be guilty. Therefore, the<br />

Jabberwocky must have told the White Knight that C told the truth,<br />

and the White Knight then knew that B must be guilty.<br />

ANOTHER CASE Again, since A told the truth and accused<br />

one of the others, he must be innocent. Now, if the White Knight<br />

had been told that C told the truth, then, without further information,<br />

he would have known that B was guilty (as we have seen in the<br />

solution of the last problem). But the White Knight could not,<br />

without further information, tell who was guilty; therefore, he must<br />

have been told that C lied. Then he was told whom C accused, and<br />

this enabled him to know who was guilty. If he had been told that C<br />

accused A, he couldn't have known whether B or C was guilty. So he<br />

must have been told that C accused B, which means that B must be<br />

innocent (since C lied), and since A is also innocent, C must be<br />

guilty.<br />

176

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