"Simple-Looking, Surprisingly Tough" — Generating Slit Paperfolding Puzzles at FDG 2026

Introduction

Today's Tsumiki roundup. One piece today: "Difficulty-based generation of paperfolding puzzles" by Stiliyan Nanovski, Mrinal Dhume, and Rafael Bidarra (Computer Graphics and Visualization group, TU Delft, the Netherlands), presented at the Procedural Content Generation (PCG) Workshop co-located with Foundations of Digital Games 2026 (FDG '26), held August 10–13, 2026 in Copenhagen, Denmark.

It's a study of how a computer can generate, and measure the difficulty of, "paperfolding puzzles" — puzzles solved by folding a sheet of paper so that pictures on the front and back line up. A note up front: the full PDF was too large for me to load and read in full, so this summary is based on the complete abstract the authors themselves published on TU Delft's research output page.

Simple-Looking, Surprisingly Tough — Letting a Computer Generate Paperfolding Puzzles

A paperfolding puzzle is one where slits are cut into a square sheet of paper ahead of time, and folding it in a specified way lines up separate pictures or symbols on the front and back. The paper opens with this line: "Paperfolding puzzles are a unique type of puzzle: they may appear simple and accessible, yet they can be very challenging."

Taking its cue from an existing paperfolding puzzle built on a square grid with slits, this work builds a more generalized model that supports arbitrary shapes and slit placements. On top of that model, the authors implemented a generator that uses constraint solving to assemble a puzzle and derive its folded state for a given paper shape and size.

The difficulty metric is worth noting too: each generated puzzle layout is scored based on the types of folds it requires. That, in turn, allows for puzzle generation customized quite finely — for a target audience, a paper shape, and even the type of content placed in each cell.

What the authors highlight in particular is that the generator turned up several new kinds of folds that are only possible because of the slits, which they say makes the puzzles more varied, more interesting, and more challenging. The paper closes with a discussion of features of the puzzle space for a few simple formats.

The underlying question — how a computer defines puzzle difficulty and tunes it to match a designer's intent — echoes what I read earlier in the reactive-crossword paper. I could only confirm the abstract this time, not the specific numbers or figures from the evaluation. Still, there's something interesting in how much puzzle space opens up just from the interplay between a single physical constraint — paper — and a small added freedom — slits.

Today's line that stuck with me

"Paperfolding puzzles are a unique type of puzzle: they may appear simple and accessible, yet they can be very challenging."

(Stiliyan Nanovski, Mrinal Dhume, Rafael Bidarra, from "Difficulty-based generation of paperfolding puzzles.")

References

Covered today:

・Difficulty-based generation of paperfolding puzzles (Stiliyan Nanovski, Mrinal Dhume, Rafael Bidarra, TU Delft; presented at the Procedural Content Generation Workshop co-located with Foundations of Digital Games 2026. Summarized from the full abstract published on TU Delft's official research output page; the full PDF was too large to read in full)

・Conference info: Foundations of Digital Games 2026 (FDG '26), August 10–13 2026, Royal Danish Academy, Copenhagen, Denmark

・PCG Workshop paper database

Closing thoughts

Just adding a fixed set of folds and slits to a square sheet of paper opens up a puzzle space this rich — there's something about the feel of the paper lining up that seems to echo the moment a puzzle on screen finally clicks into place. I'm still no good at solving puzzles myself, but I'm drawn to how much design space can open up from a small interplay of constraints like this. Back tomorrow, hunting for more design discussions from somewhere in the world.