Liar, Liar, Pants on Fire!

Logic Level 5

A man is visiting a village where each person either always tells the truth or always lies. There are 5 villagers standing in a row, and the man asks each of them how many of the 5 men standing in the row always tell the truth. Each villager gives an integer answer from 0 to 5 (inclusive). How many possible multi-sets of answers could the man receive from the villagers?

Details and assumptions

A multi-set is a set in which the elements are allowed to be repeated, e.g. {1,1,2,2} \{ 1, 1, 2, 2 \} . This distinction is made because a set, by definition, should contain distinct elements. The multi-sets {1,2,2} \{ 1, 2, 2\} and {1,1,2} \{1, 1, 2\} are distinct multi-sets, but come from the same set {1,2} \{1, 2\} .

Changing the order of the villagers' answers does not change the set of answers received. I.E. the multi-set {1,2,3,5,5} \{1, 2, 3, 5, 5\} is the same as the set {5,3,2,1,5} \{ 5, 3, 2, 1, 5\} .

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