We now have the complete solution in integers to the Diophantine equation:b=5-4t, s=3t+2. Choosing any integral value for t will give a solution, and all solutions in integers are of this form.
12. Lattice points onthe line of alinear equation
Our original problem, however, was further constrained in that both b and s had to be at least zero, as negative beetles and spiders do not exist. Hence there are only two feasible values of t, those being t=0 and t=1, giving us the two possible solutions of 5beetles and 2 spiders, and 1 beetle and 5 spiders. Ifwe interpret the puzzle as meaning that there is a plurality of both types of creature, we have the traditional solution:5 beetles and 2 spiders.