Four couples—JJ, KK, LL, MM—are standing in a line. Their positions are numbered consecutively from 1 to 8, and each person is holding hands with the persons on either side of him or her.
J and J are holding hands.
K and K are not holding hands.
L and L are holding hands.
One of the Ls is at one end of the line, and one of the Ms is at the other end.
Which one of the following must be true?