Let k=r22G where r=a/2.
Net field at center has components along x and y.
Config 1 (original):
gx=k(−M+2M+3M−4M)=0,
gy=k(−M−2M+3M+4M)=4kM.
F1=4kM.
Config 2 (3M and 4M swapped):
gx=k(−M+2M+4M−3M)=2kM,
gy=k(−M−2M+4M+3M)=4kM.
F2=kM4+16=25kM.
F2F1=254=52⇒α=2.