Dwarves and Goblins
In a magical land, there are only dwarves, who always tell the truth, and goblins, who always lie. You come across 4 of them (don't worry, goblins and dwarves are harmless. They simply either lie or tell the truth) named Nib, Nab, Nob, and Neb. They say the following:
: Nab is a goblin.
: Nib is a goblin.
: Exactly 3 of us are goblins.
: Exactly 1 of us is a goblin.
How many of them are goblins?
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1 solution
Notice that both Nib and Nab cannot be correct at the same time. This is because if they were, then Nib would be telling the truth and therefore Nab would be a goblin (or the other way around). Also, they cannot both be wrong at the same time. If they were, then both would be goblins and therefore both would be saying the truth. Then what we know is that only 1 of them is a goblin and the other is a dwarf.
Now, Nob and Neb are saying contradictory statements. Then at least one of them is lying. Since there's another goblin between Nib and Nab, then there are at least two goblins. This makes Neb a goblin. For Nob we have the following:
Nob is a dwarf : Then there are exactly 3 goblins. But since one of Nib and Neb is a dwarf, and since Neb is a goblin, then the third goblin would be Nob himself. This cannot happen.
Nob is a goblin : Then we know that there were at least 2 goblins before. Nob adds at least 3 goblins to the group. But there is a dwarf for sure between Nib and Nab. Then there are exactly 3 goblins. Then Nob is a dwarf. This is also impossible.
The problem is impossible to solve with the given information.