Instant Insanity

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Mensa Daily Puzzlers

For over 15 years Mensa Page-A-Day calendars have provided several puzzles a year for my programming pleasure.  Coding "solvers" is most fun, but many programs also allow user solving, convenient for "fill in the blanks" type.  Below are Amazon  links to the two most recent years.

Mensa 365 Puzzlers  Calendar 2017

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Problem Description

This program solves the 4 cube, 4 color version of the Instant Insanity  puzzle.  It was developed by Frank Armbruster and the commercial version is still available from .

Background & Techniques

Instant Insanity is a variation of an older cube arrangement puzzle and one of a large family of similar puzzles. In this one, we have four cubes with one of four colors on each face of each cube.  The objective is to stack the cubes so each column of  faces has all four colors.

Most of the online literature describes a graph search algorithm which can be applied to find solutions without the aid of a computer.

I imagine that the "trial and error" approach to solving the puzzle led to its name, although "Eventual Insanity" might be more appropriate since there are 41,472 arrangements to check! Why 41,272?  There are 24 orientations of each cube. Check this yourself with a die by placing each of the 6 faces pointing up and for each of these rotate the 4 vertical faces (left, front, right and back) to the front.   The product 6x4 is the number of possible orientations for that cube.

For the first placed cube, we don't need to check all 24 orientations because any solution would appear 8 times. That is, rotating a solution stack with each of the 4 faces pointing to the front would represent 4 solutions and inverting the entire stack and then rotating it would produce 4 more solutions. So for the first cube, we only need to place one face of each of the 3 axes facing up,  skipping the other 21 possible orientations. The other three cubes must be checked in each of the 24 orientations, so the total number of configurations to check is 3 x 24 x 24 x24 = 41,472.

Version 1 of this program takes advantage of the computer's speed to check all 41,472 arrangements looking for solutions.  Four sample cube sets are included, plus a sample text file which maybe used as a model to input additional sets.  Future program versions may add better graphics, other cube set sizes, and a cube set generator.

Non-programmers are welcome to read on, but may want to jump to bottom of this page to download the executable program now.

Programmer's Notes:

This program was about the right size to provide a moderately challenging problem that could be solved (and coded) in 3 or 4 days of spare time programming. 

When the Search button is clicked we set up cube definitions, Cubes  to be modified as we search from the OrigCubes definition..  Each cube is defined by a 6 character string representing  the faces in a particular order.  I chose the 6 characters to represent the colors of the Top, Left, Front, Right, Back, and Bottom faces in that order.   Cube sets are defined as TCubes type is defined as an array [0..3], of string[6] types.

SearchBtnClick calls recursive depth-first search procedure CheckNext to place the next cube in all of its orientations.  CheckNext creates the next orientation for cube N and calls itself to check cube N+1.  When the 4th cube has been placed,  function CheckSolved is called to test if this arrangement could be a solution.  If each of the four visible face directions contains all four color across the 4 cubes, this looks like a solution.  Function IsUniqueSolution is called just to make sure that we have not already encountered this solution.  IsUniqueSolution may not be smart enough yet to catch all duplicate solutions, but it will catch the case where the same colors appear on opposite faces for two different adjacent faces.  (For example GRGR colors on the Left, Front, Right, and Back faces could produce two apparently duplicate solutions when the cube is rotated 180 degrees.) 

For efficiency a doubly indexed array,  Targets,  indexes the face numbers to move to top of cube (position 1 in the cube string). TFace type defines a 6 integer array to specify the target positions for each face of the source cube. So, for example, Targets[2] is a TFace array which specifies the target locations for each of the 6 faces when face 2 is rotated to the top of the cube. Values are initialized by the InitFaceTargets procedure which applies successive rotations to fill in the target positions for each of the faces 2 through 6 is to be moved to position 1 (the top face).  Within CheckNext , calls are made to MoveFaceToTop for each face 2 through 6 to run through the Targets array and efficiently rotate the faces.  For each face on top it calls RotateCubeRight to rotate each of the visible faces to each of the 4 visible positions.   

Running/Exploring the Program 

bulletDownload source
bulletDownload  executable

Suggestions for Further Explorations

Graphic cube displays  (input and solution)
.Generalize number of cube (and colors) in the set
Add button to generate new random cube sets
Search time could be reduced by pruning the search space, I.E. if the orientation a cube being tested contains a duplication of a color of any previously placed cube in any column , there's no need to test orientations of the remainder of the cubes.   


Original:  January 8, 2010

Modified:  May 15, 2018

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