I’m looking for the kind of problem that tests mathematical thinking, not necessarily mathematical knowledge. Appropriate for a smart middle schooler. An example is estimating the value of pi given graph paper, a six sided die, and a lot of time. The student is given a short intro to the nature of random numbers (the difference between generating one from seed and generating one from a predictably random physical operation), and he knows that a quadrant of a circle with radius 1 is pi/4.
Thanks