The spider essentially travels on the hypotenuse of a triangle with the sides `A` and `B+C`.
For it to be the shortest path the condition `A <= B+C` must be true.
The amount of integer-cuboids for a given value M is "All integer-cuboids with `A=M`" plus integer-cuboids(M-1).
In our loop we start with `M=1` and increment it in every step.
We also remember the last value (for `M-1`) and loop until the value exceeds one million.
For a given value `A = M` we go through all possible `BC` value (`0 <= BC <= 2*A`) and test if `M^2 + BC^2` is an integer-square.
If such a number is found and `BC <= A` then this means we have found `BC/2` additional cuboids (there are `BC/2` different `B+C = BC` combinations where `B <= C`)
If, on the other hand `BC > A` then we have only found `A - (BC + 1)/2 + 1` additional cuboids (because the condition`A <= BC` must be satisfied).
One of the more interesting parts was the `isSquareNumber()` function, which test if a number `x` has an integer square-root.
To speed this function up *(it takes most of the runtime)* we can eliminate around 12% of the numbers with a few clever tricks.
For example if the last digit of `x` is `2`, x is never a perfect square-number. Or equally if the last hex-digit is `7`.
In our program we test twelve conditions like that:
