Four Cubes Two Puzzles (Instant Insanity)

 

Fig 1 - Four cubes with all faces decorated by 1, 2, 3 or 4 dots

Fig 2 - Puzzle #1: 1x1x4 (left), Puzzle #2: 1x2x2 (middle), pictures shown do not meet dot arrangement requirements described in text.  Orientations F, B, L, R, T, D used in this post (right)

Introduction

I was introduced to Instant Insanity puzzles by Mr. James Kerley, and I’m excited to share my design with you here. After learning, coding, and optimizing the design several times, here’s one I created for DIY laser cutting. This puzzle uses four cubes, as shown in Fig 1 above, and all the faces (24 in total, 4x6) are decorated with 1, 2, 3, or 4 dots (we’re using dots instead of colors for laser engraving, while traditional Instant Insanity puzzles use color). The goals for the two puzzles are::

• puzzle #1 - (same as a typical Instant Insanity puzzle) stack all four cubes into a 1x1x4 block as shown in Fig 2 (left). Then rotate each cubes until 
• all four 1x4 large vertical sides (F, B, L, R) each contain 1, 2, 3 and 4 dots (order not important), without repeating any.
• the T (top) side, D (down) side and internal faces do not matter.
• puzzle #2 - stack all four cubes into a 1x2x2 as shown in Fig 2 (middle). Then reposition and rotate each cubes until the following 4 sides of the stack each contains 1, 2, 3, and 4 dots (order not important) without repeating any
• F (front) 
• B (front)
• L (left) and R (right) together, that is, two vertical small sides together
• T (top) and D (down) together, that is, two horizontal small sides together
• all internal faces do not matter.

There’s a unique solution for both puzzles, considering standard physical symmetries (like permuting the cubes or rotating/flipping the entire stack). Perhaps someone will find another pattern that could become a third puzzle!

Fig 3 below shows the dot patterns on all 24 faces of the four cubes.

Fig 3 - the dot patterns on all 24 faces, 6 on each cube

The laser cut files and assembly instruction are all available at ATOMM.

Background - Instant Insanity and Related Puzzle

Instant Insanity has a fascinating history spanning more than 100 years. It involves four cubes and four colors, with each face featuring one color. Similar to our puzzle #1, the goal is to arrange these four cubes in a column (1x1x4) so that each side of the stack (front, back, left, and right) displays all four colors. The standard Instant Insanity puzzle has the following characteristics:

• It has a unique solution up to standard physical symmetries
• Each cube has all four colors, but just so you know, the dot patterns in Fig 3 show that Cube #3 doesn’t have 4 dots, so our puzzle doesn’t strictly qualify as Instant Insanity.

Also, it’s possible to arrange the four cubes of the standard Instant Insanity into a 1x2x2 shape with some patterns, which is different from our puzzle #2 we discussed earlier.

The standard Instant Insanity shows only one way to arrange the colors on 24 faces. Here are some different versions of this type of puzzle with different color layouts:

• Mutando - Besides the standard 1x1x4 puzzle, it also makes a 1x2x2 block where each face has one color. But, one of the cubes doesn’t have all four colors, so it’s not strictly an Instant Insanity puzzle.
• Mutando of Insanity - This tries to change the Mutando puzzle to make sure all four colors are in all four cubes. But, its 1x1x4 puzzle has two solutions.
• Beat the Sea Crate - This is used in the CBS Survive show. It has four pairs of opposite sides with the same color (standard Instant Insanity has two), so it’s easier to solve. Plus, it has two solutions.
• Dorobo, and Drive Ya Crazy - These use 5 and 6 cubes, and solutions are not unique.

In additional to cubes, the idea also extends to other shapes, such as 6 hexagon (or octagon) rings with 6 colors (or 8 colors), and platonic solid. 

How Do You Solve it?

Trying everything by hand can be really time-consuming because there are thousands of different ways to arrange the 4 cubes. Luckily, there’s a lot of information available that can help you solve it faster if you take a guided approach. Here’s a quick summary of some of those methods:

1. graph theory - a general approach to solve this puzzle by hand
2. understand the colors distribution and their spatial arrangement to significantly reduce the number of trial-and-error - also a general approach
3. computer code - a software to generate all possible solutions for 4 cubes into 1x1x4
4. short cut - an approach works for standard Instant Insanity, but unlikely to work on its variants

So above general approaches #1-#3 can be applied to our puzzle #1 and possibly #2 as well. Hope you enjoy this puzzle. Happy puzzling!