Sum letter and digit, using A=1, B=2, ...
A2: 1+2 = 3
F3: 6+3 = 9
The difference is 6. It is even, so intersections exist.
Half of the difference is 3. That is the delta.
To find the 2 intersections:
A2 has smaller sum => add 3 (the delta) to A and to 2. A+3, 2+3 = D5.
F3 has larger sum => subtract 3 from F and 3. F-3, 3-3 = C0.
In that case it ...
As many others have pointed out, the best idea is to learn to visualise the board better.
But since there is a neat mathematical answer, let's start by converting the letter coordinates to numbers, with A=1, B=2 etc. Then:
(TL;DR:) Take the sum of coordinates of one square, and the difference of coordinates of the other, and find the square that matches both....
First step: check if both squares are white or black,
Write a2 as (1,2), then 1 + 2 is odd hence a2 is white
Write f3 as (6,3), then 6 + 3 is odd hence f3 is white
Now, the squares on the diagonal (1,2) are the squares with a difference of 1
(a, a + 1) (and in more general the upright diagonal from (a,b) are those with difference |b-a|. For the squares on ...
X = (x1 + x2 + y2 - y1)/2 and Y = X + y1 - x1
Using this formula, we can calculate intersecting square of any two squares on chess board.
a2 > (1, 2) and f3 > (6, 3) [assuming x co-ordinate a =1, b=2, c=3....f=6, g=7, h=8]
Note: You should always consider the left side point (square) as to be the first point
So, X = (1+6+3-2)/2 = (10-2)/2 =...
Actually the accepted answer is not correct. Where do the diagonals from a4 and g4 intersect? There are two solutions, d7 and d1. It is easy to modify @Hauke Reddmann's algebra, but it seems to me much easier (and more useful) to try and improve your visualization.
The math formula is relatively easy (intersection of two straight lines,
even with fixed slant), but I assure you I can visualize it much faster
on the board than solving it, even if I'm a lousy visualizer!
Replace the letters with numbers: 12 / 63 \ (These are x,y coordinates)
12 is the upward diagonal (you didn't specify but it's obvious)
Since it is ...