MathDB

How many ways are there to fill in the

8

spots in the picture with letters

A, B, C

and

D

, using two copies of each letter, such that the spots with identical letters can be connected with a continuous line that stays within the box, without these four lines crossing each other or going through other spots?
The lines do not have to be straight. https://cdn.artofproblemsolving.com/attachments/f/f/66c30eaf6fa3b42c5197d0e3a3d59e9160bb8e.png

Problem Statement