Algorithm to get the maximum size of n squares that fit into a rectangle with a given width and height (http://math.stackexchange.com/questions/466198/algorithm-to-get-the-maximum-size-of-n-squares-that-fit-into-a-rectangle-with-a) #WIP

squares.c

int main(){
    double x=5, y=6, n=7;//values here
    double px=ceil(sqrt(n*x/y));
    double sx,sy;
    if(floor(px*y/x)*px<n)  //does not fit, y/(x/px)=px*y/x
            sx=y/ceil(px*y/x);
    else
            sx= x/px;
    double py=ceil(sqrt(n*y/x));
    if(floor(py*x/y)*py<n)  //does not fit
            sy=x/ceil(x*py/y);
    else
            sy=y/py;
    printf("%f",MAX(sx,sy));
    return 0;
}

squares.rb

def values(x = 5.0, y = 6.0, a = 7.0)
    n = (a / 4.0).ceil
    px = ( Math.sqrt( n * x / y) ).to_f.ceil
    sx = 0.0
    sy = 0.0

    if (px * y / x).floor * px < n # does not fit, y/(x/px)=px*y/x
        sx = y / (px * y / x).to_f.ceil
    else
        sx = x / px
    end

    py = ( Math.sqrt(n * y / x) ).to_f.ceil

    if (py * x / y).floor * py < n # does not fit
        sy = x / (x * py / y).to_f.ceil
    else
        sy = y / py
    end
    # printf "%f", [sx, sy].max
    v = [sx.round(2), sy.round(2)].max
    printf "%f", v
    return v
end