= Solution
The third term is $2F(11)\cos[2\pi(x+y)]$. To reinforce a maximum at $(x_0,y_0)$ from the preceding table, its sign should be
$$
S(11)=(-1)^{2x_0+2y_0}=S(10)S(01).
$$
Hence the <direct-methods triplet relationship> is $S(10)S(01)S(11)\simeq+1$ for the strong reflections under consideration. This maximizes constructive density at shared atomic positions. For weak or competing reflections the relation is probabilistic rather than an unconditional algebraic theorem.
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