Having fun with riddles!

  • The sequential shooters

    There are N people indexed by $1,..,N$ (because down with the zero-indexers! Long live Peano!) standing in a circle. They’re standing such that $i$ is between $i-1$ and $i+1$ (unless $i \in{1,N}$, for obvious reasons).

    Then starting with $1$ and going around the circle in turn, each person shoots the person directly to their left. This stops when there’s...

  • The Sequential Doors and The Data Science Analogue

    This post is going to be something of a combination riddle and blog post.

    The setup

    There are $N$ doors indexed by $1,..,N$ along a wall and they’re all closed. Then for each $i\in{1,2,\dots,N}$, you toggle every $i$ door. So at first ($i = 1$) you toggle every door. Then $i=2$ you toggle every second door – the even...

  • Quantile Regression and Quantiles of Loss


    If you’ve ever read any papers referring to quantile regression (QR), you undoubtedly have read “MSE yields means, MAE yields medians, and QR yields quantiles”. But what they hell does that even mean? Like not just hand-wavy bullshit, but really, what does that mean? After all, these are just loss functions and therefore don’t yield anything at all....