About Almost Obvious · Almost Obvious

I use this website as a diary: a place to collect questions, follow ideas, and share things that catch my curiosity. Often that means a mathematical problem, a proof, or an experiment; sometimes it is simply an idea I want to spend a little more time with.

The name Almost Obvious is a nod to those moments when a result seems clear, but the proof takes a little more thought. The small question below is a good place to begin.

A small question to start

Three cups sit in a row, all facing down. On each move, turn over exactly two cups. Can you get all three facing up?

Three cups

0 moves · 0 of 3 up

Select two cups, then press Flip selected. Select a cup again to deselect it.

Info

Select two cups, then Flip selected. Each move flips exactly two. Undo reverses the last flip; Reset turns all cups down.

Select two cups to begin.

Hint

Count the cups facing up. What can a move do to that number?

Solution

Each move changes the number of upward-facing cups by −2, 0, or 2, so it stays even; three is odd, making the goal impossible.

That is the kind of moment this notebook is about: a little experimentation, then a reason that explains every possible attempt.

Find your way around

Posts come in two forms:
- Problems begin with a question. When hints or solutions are included, they stay tucked away until you choose to open them.
- Explorations follow an idea through examples, diagrams, code, and experiments.
Learning offers courses built around compact explanations, interactive visuals, worked examples, and practice. Start with Calculus for Engineers and Scientists, then work through the problems at the end of each module.
Puzzles give you something to play with, from tiling a floor to finding a winning path in Hex.
Gadgets provide practical tools for work and study, including an exam clock, a Pomodoro timer, and ambient sound.
Research collects my work in stochastic analysis and mathematical finance.

Reading the problem thumbnails

The thumbnails beside problems give a rough sense of difficulty. A simple circle suggests a more approachable question; increasingly woven loops suggest more demanding reasoning or a less familiar insight.

Difficulty depends on your background and the insight you happen to spot. A short solution can still take a long time to find, so take these marks as an invitation to explore at your own pace.

About me

I’m a PhD candidate in Mathematical Finance at the University of Calgary. My research is in stochastic analysis and partial differential equations, and I teach mathematics. This notebook gives me a place to share the questions and ideas I encounter along the way.

For my education, teaching, and professional experience, see my LinkedIn profile.

Get in touch

Have an interesting problem, a different proof, or a correction to suggest? Send a note.