### Puzzle 49 Solution

Note that 9 people are giving 7 different answers, and at most 1 answer is correct, so there are at least 6 liars.

Suppose there are 6 liars. Then Debbie and Gilly are telling the truth and the 7 other villagers present are liars. But 7 > 6, so this assumption is wrong.

Suppose there are 7 liars. Then Ben is telling the truth and the 8 other villagers present are liars. But 8 > 7, so this assumption is wrong too.

Suppose there are 8 liars. Then the 9 villagers present are all liars. but 9 > 8, so we rule out this assumption.

Suppose there are 10 liars. Then Andy and Isaac are telling the truth, so there are at most 9 liars. But 9 < 10 so this assumption is wrong.

Suppose there are 11 liars. Then Eric is telling the truth, but that means there are at most 10 liars. 10 < 11 so this assumption is wrong yet again.

Hence, the only correct answer is that there are 9 liars, and only Jessie and Kevin who were not present are truthtellers.

Answer: 9

Suppose there are 6 liars. Then Debbie and Gilly are telling the truth and the 7 other villagers present are liars. But 7 > 6, so this assumption is wrong.

Suppose there are 7 liars. Then Ben is telling the truth and the 8 other villagers present are liars. But 8 > 7, so this assumption is wrong too.

Suppose there are 8 liars. Then the 9 villagers present are all liars. but 9 > 8, so we rule out this assumption.

Suppose there are 10 liars. Then Andy and Isaac are telling the truth, so there are at most 9 liars. But 9 < 10 so this assumption is wrong.

Suppose there are 11 liars. Then Eric is telling the truth, but that means there are at most 10 liars. 10 < 11 so this assumption is wrong yet again.

Hence, the only correct answer is that there are 9 liars, and only Jessie and Kevin who were not present are truthtellers.

Answer: 9

## 1 Comments:

At 1:39 PM, wdmtest said…

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