Let the number of males and females in the party be x and y, respectively.

Then. xy = 24  …(i)

⸫ Number of hugs among the males = x (x - 1) / 2

and number of hugs among the females = y (y - 1) / 2

⸫ Total number of hugs at the party = Numbers of hugs among the males + Number of hugs among the females

= x (x - 1) / 2 + y (y - 1) / 2  …(ii)

From Eq. (i), the value of xy can be (1, 24), (3, 8), (2, 12), (4, 6), (6, 4). (8, 3), (12, 2) and (24, 1).

By taking one of these values and putting in Eq. (ii), we get

Total number of hugs at the party = 6(6-1) / 2 + 4(4-1) / 2 = 15 + 6 = 21