16/7 = 2 2/7 or 2 and 2 remainders 25/7 = 3 4/7 or 3 and 4 remainders 36/7 = 5 1/7 or 5 and 1 remainder 49/7 = 7 64/7 = 9 1/7 or 9 and 1 remainder 81/7 = 11 4/7 or 11 and 4 remainders
This tells us that the only possible remainders for a two digit square number divided by 7 are 1, 2 and 4 If Doris got 6 and Horace got 3, they must have made a mistake.