Glance at the first and second statement again; they are contradictory. Both can be true together though. Also both of them cannot be false which means that Tim stole cat and his statement will be true. But it has been already deduced that the one who stole cat was telling a lie thus it can’t be possible.

Let us consider the situation again. It may be that Tim stole a hen or a dog. Assume that he stole hen. In such a case the statement of Tim will be false. But we know that the person who stole hen told the truth, thus it is contradicting our assumption and so cannot be correct.

Considering everything, now we can say with confidence that Tim stole the dog.

Now it means that the statement by Robin is completely false and the statement by Steve is true which depicts that the cat and hen are stolen by these two. Also we know that the one who stole hen is true and the one stealing cat is a liar.

Thus we now know that Robin stole cat and Steve stole hen.

Each person can shake hands with 23 other people, so we have 24 × 23 possible combinations. But because it takes two people to make a handshake, we must divide this product by 2, so we get (24 × 23)/2 = 276.