Square Deal

On Thursdays the 16 members of the Square Deal Card Club play four tables of bridge. Each player has a number from 1 to 16 on a score card. The eight male members always have even numbers and the females have odd numbers. All partners are male-female pairs.

One Thursday Jan noticed that she and her partner, Dan, had card numbers that were consecutive integers and added to a perfect square. Her opponents' card numbers also added to a perfect square. What's more, the four card numbers at her table were consecutive integers.

This interesting fact caused Jan to check the other three tables. Amazingly, all of the partners' sums at all tables were perfect squares. However, none of the partners' cards had numbers that added to a number greater than the sum of the numbers on Jan's and Dan's cards.

At one other table, the four players had card numbers that were consecutive integers. The player holding card number 10 was sitting next to the player holding card number 16.

Identify the card numbers at each of the four tables.

Reference from Greenes, Carol, Linda Schulman, Rika Spungin, Suzanne Chapin, Carol Findell. Mathletics: Gold Metal Problems. Providence RI: Janson Publications Inc., 1990. p. 21.