Ball Lock Puzzle

thingiverse

Here's an exciting new puzzle that I'm sure will challenge even the most experienced puzzlers. It's called the z=xy puzzle, and I've been calling it a complex version of my 2-piece cube puzzle, with the added magic of a ball lock. The z=xy puzzle combines elements of mathematics, magic tricks, and logic puzzles in a unique way. Here are some reasons why you'll love this puzzle. Firstly, when the cube is locked by rotating the ball, it seems impossible to open it again. You can close and open the cube multiple times, but as soon as the audience member takes it over and tries to pull it apart, they won't be able to. The puzzle requires two moves to solve: 1) secretely rotate the ball from the back side of the cube as you hand it over; 2) invisibly flick the cube itself 180 degrees from its original position. There are two secrets behind this amazing puzzle: 1) When I close the cube and hand it over, I secretly rotate the ball to lock it in place. 2) The profile of each hemisphere viewed from the pole is non-circular, making it impossible to predict which direction the hemispheres will move when opened. Here's a breakdown of how this works: 1. Bisecting the ball symmetrically means that the two halves can only separate along one axis. When combined with the fact that each hemisphere has a counterintuitive non-circular profile, the result is a unique and seemingly paradoxical puzzle. 2. The saddle-shaped surface that bisects the sphere is a hyperbolic paraboloid - or in simpler terms, z=xy. It's amazing to see how pure mathematics can lead to such innovative applications. With this puzzle, you'll not only experience a fun challenge but also gain an understanding of complex mathematical concepts like spherical symmetry and counterintuitive profiles. If you want to bring your skills up a notch, print this file at 0.2 mm layer thickness with support, as this is essential for creating a smooth exterior on the ball housing. Use plenty of fan while printing so that the overhangs come out smooth. If needed, use sandpaper to round off the bottom surface and create a perfectly spherical ball that rotates smoothly within its casing. To assemble this beautiful puzzle, you need to align the hemispheres in their default position (pointing the saddle upwards), then rotate them by 90 degrees so that they are aligned with each other but point towards the housing opening. Make sure both halves fit snugly together before finalizing your work. If you don't have access to a 3D printer, Shapeways has an official store page for these puzzles - just remember that the puzzle needs two halves if printed by them! They also modified it to ensure compliance with minimum thickness rules, which resulted in slightly different but equivalent designs. You can choose your desired color combination.