As part of his exploration of the world of puzzles for his excellent book The Puzzler, author A.J. Jacobs set out on a rather quirky mission: He wanted to commission the world’s most challenging puzzle. The job ultimately went to puzzle constructing legend Oskar van Deventer, and the result is a device called the Jacobs’ Ladder.
How difficult is this puzzle? Let’s back up a moment.
Did you ever download a puzzle app for your phone or tablet, and find that you are encouraged not only to solve each level but to do so in a minimum number of moves? Yes, you can slide the doohickey into the whatever, avoiding all the traps along the way, but can you do it in six moves or less? The 6 sits in the upper corner of the screen, mocking you. You solved the level in eight moves. Do you move on? If you are me: Heck, no. You reset the level and try to find an improved solution.
Similarly, there are classic puzzle games like the Tower of Hanoi, where you have to move all of the discs from one peg to another, always keeping smaller discs on top of larger ones. These games have been the subject of much mathematical analysis — it is reasonably well-known that a three-disc version of Tower of Hanoi can be solved in seven moves. A four-disc game can be solved in fifteen moves. If you have five discs, you’ll need 31 moves. That’s if you take the most direct route, of course. Make a wrong turn and the puzzle might take you far longer.
You might suppose that a Rubik’s Cube would take longer to solve than a five-disc Tower of Hanoi, but you would be wrong. Back in 2010, computer scientists figured out that no matter how scrambled your cube is to start, you can get it to a solved position in a minimum of 20 moves.
The very hardest puzzles, of course, have a much higher number of minimum moves. Before the Jacobs’ Ladder was created, the acknowledged contender for the record was a Chinese ring puzzle with 65 rings, owned by collector Jerry Slocum: Solving it perfectly will take you a full 18,446,744,073,709,551,616 moves. As Slocum notes in this New York Times article, at one move per second, that would take about 56 billion years. But, you know. By moving faster maybe you could cut that time in half.
So Slocum’s puzzle takes longer to solve than the age of the universe, but Jacobs’ Ladder beats it somehow? Indeed it does. The goal of Jacobs’ Ladder is to get a corkscrew-type thingie from the bottom of the device all the way to the top, traversing a number of pegs along the way. This will require you (if you take the shortest possible route) to make 1,298,074,214,633,706,907,132,624,082,305,023 moves. That’s over a decillion moves, and needless to say it leaves Slocum’s 18 quintillion moves in the dust. I can’t improve on Oskar van Deventer’s own description of just how long this is, so let’s break out the quote box, from this article by A.J. Jacobs in the Atlantic:
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.
You might wonder what the point is of a puzzle that, at the end of the day, can’t really be solved. Well, in the above-linked article, Jacobs points to the enjoyable meditative aspect of sitting and turning the pegs, embarking on a slow, slow journey down the solving path. Fair enough. The puzzle is also a physical encapsulation of how hard it is for humans to envision enormous numbers. You can hold it in your hands and try to get your brain around the concept of 40 septillion years.
But for sheer solving pleasure, I think I’m going to stick to this app on my phone. Surely this time I’ll figure out how to beat this level in a mere six moves.