April's ClueJo Logic Problem - Target Practice

Col. Mustard, black, 9+7+5 = 21
Mr. Green, gold, 5+3+0=8
Miss Scarlet, blue, 7+3+1=11
Mrs. Peacock, white, 7+5+3=15
Mrs. White, red, 9+5+0=14
Prof. Plum, green, 9+9+1=19

April's Spring Special - Knights, Knaves, & Jesters

A. It is impossible for either a Knight or a Knave to say, “I’m a Knave,” because a Knight wouldn’t make a false statement that he was a Knave, and a Knave wouldn’t make a true statement that he was a Knave. Therefore, A never did say that he was a Knave, so B lied when he said A said that he was a Knave. Hence, B is a Knave. Since C said that B was lying, then he is telling the truth so he spoke the truth; hence, C is a Knight. It is impossible to tell what A is.

B. The answer is the same - B is a Knave and C is a Knight, although the reasoning is a bit different here. The first thing to observe is that B and C must be of opposite types, since B contradicts C. So of these two, one is a Knight and the other is a Knave. Now, if A were a Knight, then there would be two Knights present, hence A could not have lied and said there was only one Knight present; but then A, being a Knave, couldn’t have made that true statement. Therefore, A could not have said there was one Knight among them. So B’s statement to what A said is false, and B is a Knave and C is Knight, and A must also be a Knight.

C. Suppose A were a Knave. Then when A makes the statement “At least one of us is a Knave” it would be false since Knaves always lie; hence, they would both be Knights. Thus, if A were a Knave he would also be a Knight, which would be impossible. Therefore, A is not a Knave, he is a Knight, and since he is a Knight, then he tells the truth when he says at least one of them is a Knave. Therefore, A is a Knight and B is a Knave.

D. A must be a Knave, for if he were a Knight, then it would be true that all three are Knaves and hence that A too is a Knave, but then he’d be both a Knight and a Knave, which is impossible. So A is a Knave and made a false statement that all three were Knaves, so at least one of them is a Knight. Now, suppose B were a Knave. Then A and B would both be Knaves, so C would be the Knight, which would make B’s statement true, but if it were true, then B would also be both a Knave and a Knight, which is impossible. Therefore B must be a Knight, and from his statement, he is the only Knight, so A and C are Knaves.

E. In the 2nd part, if A says, “All of us are Knaves,” and B says, “No, exactly one of us is a Knave,” then it can’t be determined what B is, but we can determine what A and C are. A must be a Knave for the same reasons given above, so there must be one Knight among them. Now, either B is a Knight or a Knave. If he is a Knight, then it would be true that exactly one of them is a Knave, which we’ve already shown to be A, so that would make C a Knight. On the other hand, if B is a Knave, then C must be a Knight, since all three can’t be Knaves. However, it can’t be shown for certainty whether B is a Knight or aKknave, but in either case, C is a Knight.

F. To answer this one, one must use the information given that the stranger knew the answer after the inhabitant’s response. Suppose the speaker - lets call him A - had answered, “Yes.” Could the stranger have known whether at least one of them was a Knight? Actually, no. For it could be that A was a Knight and answered truthfully when he said “Yes” , or it could be that both were Knaves, in which case A would have answered falsely with a “Yes.” Thus, by getting a “yes” answer, the stranger really couldn’t have no way of knowing whether A was a Knight or a Knave, so A answered “No” to the stranger’s question. Therefore, the stranger can now know what A and the other inhabitant - lets call him B - are. If A were a Knight, he couldn’t have truthfully answered “No,” so A is a Knave. Since his answer is “No” and he is a Knave, then he is a liar, so there is at least one Knight present. Hence, A is a Knave and B is a Knight.

G. A cannot be a Knight, because a Knight would never say that he was a Jester. So A is either a Knave or a Jester. If he was a Jester, then B’s statement would be true; hence, B is either a Knight or is a Jester, but B can’t be a Jester (since A is, according to this supposition) so B is a Knight. This would leave C a Knave. But a Knave cannot say that he is not a Jester (because a Knave really isn’t a Jester, so he’d be telling the truth, which would make him also a Knight). Therefore, A cannot be a Jester; hence, A is a Knave. Then B’s statement is false, so B must be a Jester, which leaves C as the Knight.

H. B says that “I sometimes tell lies and sometimes tell the truth,” so if B’s statement is true, he is a Jester and the other two would be lying and would be Knaves, but A and C gave opposite replies, so they couldn’t possibily both be Knaves; therefore, B is lying and since he can’t be a Jester, then he is a Knave. Since A said that B always told lies, then he would be a Knight as this would be true. Since C said that B always tells the truth, that would be a lie, but since we know there were one of each - Knight, Knave, and Jester, and A is a Knight and B a Knave, then C would be a Jester, and this was one of those times the Jester decided to lie.

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