Question 15
The first five instances of a pattern involving three squares are shown below. Find $B+D-A-C$.
$$4^2+12^2+6^2=14^2$$
$$4^2+20^2+22^2=30^2$$
$$4^2+28^2+46^2=54^2$$
$$4^2+36^2+78^2=86^2$$
$$A^2+B^2+C^2=D^2$$
Continue with positive bases: the first column stays constant, the second has constant first differences, and the third and fourth have constant second differences.
$$4^2+12^2+6^2=14^2$$
$$4^2+20^2+22^2=30^2$$
$$4^2+28^2+46^2=54^2$$
$$4^2+36^2+78^2=86^2$$
$$A^2+B^2+C^2=D^2$$
Continue with positive bases: the first column stays constant, the second has constant first differences, and the third and fourth have constant second differences.