How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? I originally came across this puzzle on the codeforces website.
My first question: what is the mathematics behind solving these kind of puzzles? Just plain algebra?
My second question, more philosophical: how many of you solved this instantly? I could not solve it even after a bit of googling. I am interested in developing my intuition or mathematical aptitude for solving these kind if problems. Any advice? Its been many years since I am out of college.
Some test cases for you to check your answers before you post them. Input 2 3 4 Answer 18
Input 2 2 2 Answer 7
Input 7 8 13 Answer 224
Input 985 2 2 Answer 2956