Mark Rober built a robot that solves jigsaw puzzles and pitted it against Tammy McLeod, one of the world’s faster human solvers. The design and build process is fascinating, especially the fine-tuning enabling the robot to “wiggle” each piece into its place.
When we first tried to assemble the puzzle, almost none of the pieces fit together perfectly. This was before we had corrected the errors in the computer vision code as described earlier.
However even after we improved the computer vision code, some small errors remained. Many pieces would fit together perfectly, and then you would see one that was ever so slightly out of place, and that could ruin the alignment for the rest of the puzzle if left unresolved.
To solve this, we took inspiration from humans. If you try to place a puzzle piece with your hands, you’ll find that often you need to wiggle the piece around to get it to snap into place. So we programmed the robot to do the same thing.
And then, on a Friday morning, I woke up to an email from Oskar. He had finished making the puzzle — and it worked. He had made a 55-pin Jacobs’ Ladder. Solving it would take 1.2 decillion moves1 (the number 1 followed by 33 digits). Written out, that’s: 1,298,074,214,633,706,907,132,624,082,305,023 moves.
We’d crushed the old record by 13 orders of magnitude. Oskar did some delightfully nerdy calculations on just how long it would take to solve this puzzle. If you were to twist one peg per second, he explained, the puzzle would take about 40 septillion years. By the time you solved it, the sun would have long ago destroyed the Earth and burned out. In fact, all light in the universe would have been extinguished. Only black holes would remain. Moreover, Oskar said, if only one atom were to rub off due to friction for each move, it would erode before you could solve it.
Here’s a video about the puzzle from the guy who designed and built it:
FYI: Jacobs’ book, The Puzzler, includes a “a hidden, super-challenging but solvable puzzle that will earn the first reader to crack it a $10,000 prize”. Good luck!
Small rounding error here…it’s actually 1.3 decillion moves.↩
The father-son duo of Martin and Erik Demaine make typefaces that are algorithmic, mathematical, or puzzle-like in nature. For instance, here’s their Tetris font, where each letter is made up of the seven possible Tetris pieces:
Or their newest one, Everything, where each letter can be folded into any other letter:
Everything to everything. This typeface illustrates how to fold any letter into any other letter, or more precisely, how to fold a piece of paper in the shape of any letter into the shape of any other letter. This lets you write one message inside another in a couple of ways. On the one hand, you could present the 6x6 crease patterns whose silhouettes look like one message (first text), and folding them reveals another message (second text). On the other hand, you could present the folded forms (as physical objects) whose silhouettes look like one message (second text), and unfolding them reveals another message (first text).
In a 2015 paper, “Fun With Fonts: Algorithmic Typography,” the Demaines explained their motivations: “Scientists use fonts every day to express their research through the written word. But what if the font itself communicated (the spirit of) the research? What if the way text is written, and not just the text itself, engages the reader in the science?”
Inspired by theorems or open problems, the fonts — and the messages they compose — can usually be read only after solving the related puzzle or series of puzzles.
You can check out the rest of their typefaces on their website — they include fonts with infinitely tiling letters, Sudoku puzzle fonts, and a font whose letters are made up of shapes that can be packed into a 6x6 square. So fun!
Two Puzzles by Micah Lexier consists of a pair of jigsaw puzzles, each with the die-cut pattern of the other puzzle printed on it. From Lexier’s Instagram:
They look like two of the exact same puzzles, but are in fact different. One is the image of the nine-piece puzzle foil-stamped on to the 16-piece die-cut puzzle and the other is the image of the 16-piece puzzle foil-stamped on to the nine piece die-cut puzzle.
Taking advantage of the fact that puzzle manufacturers typically use the same cut patterns to make many different puzzles, Tim Klein uses the interchangeable pieces to create surrealist mashups of puzzles.
For her project entitled Within 15 Minutes, artist Alma Haser made identical jigsaw puzzles out of portraits she’d taken of identical twins and then swapped every other piece when putting them together, creating these serendipitously fragmented portraits. She said of her first attempt last year:
So today for no apparent reason I thought I’d test out a crazy idea I had. For the project I have been switching just the faces of the identical twins, but today I decided to see what it would look like to swap every other pieces with reach other. Completely entwining the beautiful @being__her sisters. And wow, what an effect! It really make you double take at their faces, trying to decipher one for the other.
You can follow Haser’s work, including the twin puzzles, on Instagram.
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