abcd is a square. How many squares in the same plane have two or more vertices in the set {a,b,c,d} ?
I'm counting 8.
(a,b), (b, c), (c, d), (d, a) each with two other vertices not in {a,b,c,d}
(a,c) to the ne and sw
(b,d) to the nw and the se
I counted 8 too.
1 square share the vertices a and b.
1 square share the vertices c and b.
1 square share the vertices c and d.
1 square share the vertices a and d.
2 square share the vertices c and a.
2 square share the vertices b and d.
+296 
