The hottest Puzzles Substack posts right now

And their main takeaways
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Top Education Topics

“Lights Out” on a triangular grid

A Piece of the Pi: mathematics explained • 30 implied HN points • 22 Mar 26
🔬 Science Puzzles
  1. The triangular Lights Out game reduces to linear algebra over the field with two elements: pressing a button toggles bits mod 2, pressing a button twice cancels, order doesn’t matter, and any solution is a subset of buttons pressed once.
  2. Solvability and uniqueness depend on the kernel of the toggle map: if the kernel is only the empty set (ℓ=0) then every starting state has a unique solution, which occurs for certain side lengths such as 1, 3, 4, 7, 8, 9, 11, 15, 16, 17, 20, and 21.
  3. If the kernel is nontrivial (ℓ>0) there are nonzero button patterns that have no effect and some starting configurations cannot be solved; the kernel is a 2^ℓ-sized vector space over GF(2) and its patterns often form visually striking shapes like the Sierpiński triangle.

Hello World

Bram’s Thoughts • 334 implied HN points • 05 Apr 23
🕹 Technology Puzzles
  1. The user is trying out 'real' blogging for the first time.
  2. The blog posts will likely cover various engineering topics unrelated to Chia.
  3. Readers can find the user's puzzles at a specific link or play a game on a website.

Spiral Sudoku

A Piece of the Pi: mathematics explained • 60 implied HN points • 23 Jul 25
🚌 Education Puzzles
  1. Spiral Sudoku is a type of puzzle that involves filling a grid in a spiral pattern with numbers. The challenge is to ensure that every row and column has the numbers 1 to 5 without repetition.
  2. The grid is designed with specific circled positions that guide where the numbers should be placed. Understanding these positions is key to solving the puzzle successfully.
  3. This puzzle not only tests your problem-solving skills but also makes math fun and engaging. It's a great way to practice logic and critical thinking.

The Monty Hall problem: The golden goat variation

Simplicity is SOTA • 131 implied HN points • 03 Feb 25
🔬 Science Puzzles
  1. The Monty Hall problem has a new twist, focusing on a valuable goat instead of a car. In this version, knowing which goat is valuable affects your choice.
  2. Using Bayes' theorem can help calculate the probabilities in this variation. After a goat is revealed, you can reassess your chances to make a better decision.
  3. The essential lesson is to update your beliefs with new information. Recognizing how new clues impact your choices is key to making smarter decisions.
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Turning a triangle into a square

A Piece of the Pi: mathematics explained • 115 implied HN points • 11 Jan 25
🔬 Science Puzzles
  1. Henry Dudeney showed in 1902 that you can cut an equilateral triangle into four pieces and rearrange them into a square with the same area. This is a fun example of how shapes can transform while keeping their total area the same.
  2. The Wallace–Bolyai–Gerwien theorem explains how you can rearrange two shapes with the same area into each other through cutting, but Dudeney's method is unique because the pieces stay connected during the transformation.
  3. Recent research proved that you can't turn a triangle into a square using fewer than four pieces without flipping any. This shows how specific and tricky these geometric dissections can be.

Infinite Sudoku

Infinitely More • 23 implied HN points • 12 Jul 25
🚌 Education Puzzles
  1. Sudoku is typically a solo puzzle where you fill a 9x9 grid with numbers, ensuring that each number appears only once in each row, column, and 3x3 box.
  2. There's a fun two-player version called the Sudoku game where players take turns placing numbers on an empty board, trying to outsmart each other without breaking the Sudoku rules.
  3. The Sudoku game can be played on larger or different shaped boards, and there are even ideas for playing infinite versions of the game on larger grids.

#96 Puzzling design

Design Lobster • 179 implied HN points • 29 Nov 21
🎨 Art & Illustration Puzzles
  1. Jigsaw puzzles were invented by John Spilsbury, starting as educational tools for children which later became popular as a therapeutic activity during the Great Depression.
  2. Puzzle jugs from the 18th century were designed with hidden tricks to prevent spills, showcasing how designs can incorporate elements of surprise and challenge for users.
  3. Design should aim to reduce clutter and confusion, but intentional puzzlement in design can sometimes offer satisfaction and intrigue to users.

Boomerang tilings

Infinitely More • 15 implied HN points • 25 Jun 25
🔬 Science Puzzles
  1. Boomerangs are special shapes called nonconvex quadrilaterals. They can be used to explore interesting questions about tiling.
  2. The main question is whether a convex polygon can be tiled completely using just a few boomerangs. This is a challenging mathematical problem.
  3. Finding a solution to this problem requires careful thought and may not be easy. Just because one attempt fails, it doesn’t mean that it can’t be done at all.

Why are there 62,208 puzzles?

actinium226’s Substack • 4 HN points • 03 Jun 24
🔬 Science Puzzles
  1. The 'Genius Square' puzzle game has a unique selling point of 62,208 puzzles always solvable.
  2. The author explores multiple attempts to understand how the specific number of puzzles was derived.
  3. By closely examining the dice used in the game, the author reveals the mathematical reasoning behind the 62,208 puzzles.

The Parks puzzle

A Piece of the Pi: mathematics explained • 36 implied HN points • 11 Nov 24
🚌 Education Puzzles
  1. The Parks puzzle is a game where you place trees on a grid with specific rules, similar to Sudoku. Each row, column, and park needs a certain number of trees without them being next to each other.
  2. While checking if a proposed solution is correct is easy, finding that solution can be quite complex. Researchers found that the Parks puzzle belongs to a group of difficult problems called NP-complete.
  3. The puzzle can be used to model logical operations like AND and OR. This means it has connections to computer science concepts and can help explore complex problems.

Rubik’s abstract polytopes

A Piece of the Pi: mathematics explained • 18 implied HN points • 03 Mar 25
🔬 Science Puzzles
  1. Rubik's Cube can be made in different shapes, like a tetrahedron or dodecahedron, instead of just the classic cube. These variations have their own names, like the Megaminx for the dodecahedron.
  2. A new study explains how to think about these puzzles in more dimensions, counting how many different ways they can be turned or rearranged. This includes understanding shapes like the hypercube.
  3. The math behind a Rubik's Cube shows interesting patterns, like counting sticks and pieces, and this can help us understand all kinds of shapes and designs better.

Meta-knowledge

Metarational • 19 implied HN points • 26 Apr 21
🚌 Education Puzzles
  1. Meta-knowledge involves the understanding of other people's knowledge, leading to concepts like meta-meta-knowledge and common knowledge.
  2. Puzzles, like the blue eyes puzzle, are great examples to demonstrate the complexity and power of different levels of meta-knowledge.
  3. Understanding meta-knowledge is crucial in various contexts, helping to make sense of social customs and intuitions that may otherwise seem arbitrary or senseless.

I’m a Senior Software Engineer. What Will It Take For An AI To Do My Job?

Am I Stronger Yet? • 3 HN points • 20 Apr 23
🕹 Technology Puzzles
  1. Current AI systems are still lacking critical cognitive abilities required for complex jobs.
  2. AI needs improvements in memory, exploration, puzzle-solving, judgement, clarity of thought, and theory of mind to excel in complex tasks.
  3. Addressing these gaps will be crucial for AI to reach artificial general intelligence and potentially replace certain human jobs.

Tricky Appointment Timings

Metarational • 0 implied HN points • 18 Oct 23
🚌 Education Puzzles
  1. The LSAC is removing logic games from the LSAT, causing disappointment.
  2. A challenging logical game involving appointment timings for five clients.
  3. Constraints shape the schedule, posing questions to solve based on rules and possibilities.

VFYW: Horsing Around

The Weekly Dish • 0 implied HN points • 17 Jan 26
🎭️ Culture Puzzles
  1. A window-view puzzle hinged on small clues — a ‘‘Riley Oil’’ sign and a partial ‘‘Willa-’’ street name — which readers used to pinpoint a spot in Kentucky.
  2. An engaged community of sleuths swapped tips, local knowledge, and jokes while narrowing the location, showing how collective detective work makes the game fun.
  3. The writeup paired the geography hunt with regional food, including a Kentucky-style fried chicken and succotash, linking the place to its culinary culture.