Jane Street publish a puzzle every month or so. This is my solution for the April 2025 puzzle.

Problem

For a fixed \(p\), independently label the nodes of an infinite complete binary tree \(0\) with probability \(p\), and \(1\) otherwise. For what \(p\) is there exactly a \(1/2\) probability that there exists an infinite path down the tree that sums to at most \(1\) (that is, all nodes visited, with the possible exception of one, will be labeled \(0\)). Find this value of \(p\) accurate to ten decimal places.

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Spoilers ahead.

Burning (2018) is film that lingers with you. You find yourself thinking about it in idle moments, even weeks after having watched it.

Ambiguity

The film was based on a short story by Haruki Murakami, titled Barn Burning. The short story has a similar premise. Having read it, I was left with the same chilling feeling that the film gave me.

“I still run past the five barns every morning. No barn in my neighborhood has burned down. And I haven’t heard about any barn burning. December’s come again, and the winter birds fly overhead. And I keep on getting older.”

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I’ve recently started working on my master’s thesis, and as such I’ve been looking for a good way to take notes. I need to be able to capture notes on my reading, as well as any ideas or thoughts that I have. I’ve previously experimented with:

• Notion - I did like how feature rich it was, but I disliked the rigid organisation structure. I felt forced to organise everything into a heirarchical pages and sub-pages. Also, it felt like once I committed to Notion, it wouldn’t be possible to switch platforms if I wanted to.

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