There are 52 people. No one gives himself or herself, or hir spouse a calling cards, so everyone can give up to 50 cards. That's 51 possibilities, and there are 51 people Ann asks, so they have given 0, 1, 2, ... 50 cards.
Adam is not the person who exchange 50 cards, because if he did, then someone would have exchanged a card with him, and the zero can't be placed on anyone. The only way for there to be a person who exchanged 50 cards and for a person to have exchanged zero cards means that they are a couple. Say, Mr and Mrs Z.
The only way for someone to have 49 cards, and just one, is that they are a couple. One of them gave to everyone except one of the Z couple, and one received a card from everyone except one of the Z couple. Say, Mr and Mrs Y.
Repeat for another couple, 48 and 2. then 47 and 3. etc etc etc. Until Mr and Mrs B exchange 24 and 26 cards.
Adam and Ann have received one card each from every invited couple; 25 cards each.