### Brain Teasers

# Half Truthful

Three Paley brothers and three Thomson brothers operate a company that manufactures lie detectors. Three of these six men always tell the truth, and three always tell lies; neither set of brothers consists exclusively of liars. Some recent statements from the six men are recorded below. Can you find the six men's full names, and tell which men tell the truth and which tell lies?

1. Alan: "Both my brothers tell lies."

2. Boris: "Both my brothers tell the truth."

3: Chuck: "Alan and Boris are both liars."

4. Dalman: "Chuck and I are brothers."

5. Edwin: "Boris and I are brothers."

6. Finney: "Edwin tells the truth."

7. Finney: "Boris is one of the Paleys."

1. Alan: "Both my brothers tell lies."

2. Boris: "Both my brothers tell the truth."

3: Chuck: "Alan and Boris are both liars."

4. Dalman: "Chuck and I are brothers."

5. Edwin: "Boris and I are brothers."

6. Finney: "Edwin tells the truth."

7. Finney: "Boris is one of the Paleys."

### Answer

Alan Thompson, LiarBoris Paley, liar

Chuck Thomson, truthteller

Dalman Paley, liar

Edwin Paley, truthteller

Finney Thomson, truthteller

Neither set of brothers consists entirely of liars (introduction), so neither consists entirely of truthtellers, either. Boris, then, can't be telling the truth (clue 2); Boris is a liar. If Alan lies, then Chuck tells the truth (clue 3), and vice versa, so between Alan and Chuck, one is a liar and one a truthteller. By elimination, Dalman, Edwin, and Finney are, in some order, one liar and two truthtellers. If Finney is a liar, so is Edwin (clue 6), which is impossible; so Finney tells the truth and so does Edwin (Clue 6); Dalman, then, is a liar. Boris is a Paley (clue 7). Edwin is a Paley (clue 5). Chuck and Dalman are not brothers (clue 4), so one is a Paley and the other a Thomson; by elimination, Alan and Finney are both Thomsons. Finney Thomson tells the truth, so Alan Thomson is a liar (clue 1) and Chuck is a truthteller (clue 3). Boris Paley lied when he said both of his brothers tell the truth (clue 2); one of his brothers is Edwin Paley, a truthteller, so the other must be a liar - and therefore the third Paley can't be Chuck, a truthteller, so must be Dalman, a liar. By elimination, Chuck is a Thompson.

...got it?

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