The husband and wife are playing the old game of BATTLESHIP. The two-word communications consist of a letter and a number for the coordinates of where the ships are hidden, and the one-word responses are either, "Hit" or "Miss". The final four word phrase which ends the game is, "You Sank My Battleship!"
The answer to this math riddle is 21. You probably just guessed to answer this math riddle, which is fine, but you can also work it out algebraically. The two-digit number ab stands for 10a + b since the first digit represents 10s and the second represents units. If 10a + b = 7(a + b), then 10a + b = 7a + 7b, and so 3a = 6b, or, more simply, a = 2b. That is, the second digit must be twice the first. The smallest such number is 21.