8.2. In a fairy-tale country, every piglet either always lies or always tells the truth, and each piglet reliably knows whether every other piglet is a liar. One day, Nif-Nif, Naf-Naf, and Nuf-Nuf met for a cup of tea, and two of them made statements, but it is unknown who exactly said what. One of the three piglets said: “Nif-Nif and Naf-Naf both always lie.” Another said: “Nif-Nif and Nuf-Nuf both always lie.” Determine how many liars are among the three piglets.
# Answer: Two

Solution: If at least one of the statements is true, then the piglets mentioned in it are liars, which means there are at least two liars. At the same time, the one making this true statement must be telling the truth. Therefore, there are no more than two liars. In total, if at least one of the spoken phrases is true, then there are two liars. Note that this is possible, for example, if the first phrase is said by Nuf-Nuf.

If both statements are false, then those who say them are liars. This means there are at least two liars. At the same time, for each phrase to be false, at least one honest piglet must be mentioned. This means there is one, so there are no more than two liars. Thus, in this case, there are exactly two liars. Note that this situation is possible if the only honest piglet is Nif-Nif and he is silent.

Criteria: Only the answer - 0 points.

Example that there can be 2 liars, no other progress - 1 point.

Enumerative solution, missing cases - no more than 4 points.

For the absence of verification that there can indeed be two liars, do not deduct points.