MathDB

Let us consider an infinite grid plane as shown below. We start with 4 points

A

B

C

D

, that form a square.
We perform the following operation: We pick two points

X

and

Y

from the currant points.

X

is reflected about

Y

to get

X'

. We remove

X

and add

X'

to get a new set of 4 points and treat it as our currant points.
For example in the figure suppose we choose

A

and

B

(we can choose any other pair too). Then reflect

A

about

B

to get

A'

. We remove

A

and add

A'

. Thus

A'

B

C

D

is our new 4 points. We may again choose

D

and

A'

from the currant points. Reflect

D

about

A'

to obtain

D'

and hence

A'

B

C

D'

are now new set of points. Then similar operation is performed on this new 4 points and so on.
Starting with

A

B

C

D

can you get a bigger square by some sequence of such operations?

Problem Statement