Just a bit of aimless fun. I just found this interesting, so tried to implement it in Scratch. https://en.wikipedia.org/wiki/Buffon%27s_needle#Estimating_%CF%80 The project uses cloud variables to tot up the grand totals, so the result should fine tune over time.
The needle display appears jerky because of the custom loop running without screen refresh, to speed things up. I don't know whether it saves any processing time, but I'm assuming that restricting the needle to one quarter of 360 degrees gives the same result, so what the hey! (Having said that, I'm pretty much convinced that using 90 rather than 89.9999999... is skewing the result. Hmm, maybe giving it the full 360 would lessen the effect.) Another confounding factor is the thickness of the needle (1 pixel) when presumably the concept actually requires a needle of zero thickness. I haven't read the brief very thoroughly!