Problem Description

Four piles of blocks, each 6 blocks high and containing the letters "A' through "F" are scrambled versions of the "solution" stack.  For each of the 4 stacks, you are given the number of pairs that match the solution stack and the number of pairs that are reversed versions of pairs in the solution stack.  Your job is to reconstruct the solution stack. 

Background & Techniques

The "piles of blocks" aren't the random result of child's play but clues to a final solution stack. Like the rest, this final pile has 6 bricks, each with a different one of the six letters. Your job is to determine the order of the blocks in the final pile.

The numbers below the piles tell you two things:

• The number of adjacent pairs of bricks in the that column also appear adjacent in the same order in the
  final stack.
• The number of adjacent pairs of bricks that make a correct pair but are in the wrong order.

This puzzle was adapted from "Logical Puzzles - 320 Teasing Tests of Your Mental Acumen", Chartwell Books
Inc., 2006.

If you want to try to solve it yourself, you can enter letters A through F in the solution column and the current counts of "Inorder" and "Reversed" matches against each of the other stacks will show up in the "User Guesses" box.  When your stack's counts of Inorder and Reversed  pairs matches the numbers comparing each stack to the solution, you've solved it! 

The "Solve" button will solve the puzzle by searching through all 720 possible ways to arrange the 6 blocks in a stack (6 choices for the first block, 5 choices for the second, etc. 6x5x4x3x2x1=720).

The "Create" button will create new random puzzles with unique solutions.

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

{Program description to be added later - no time today, so it's this or not post  at all.}

Running/Exploring the Program 

• Download executable
• Download  source

Suggestions for Further Explorations

• I had originally planned to use a stack image with blank blocks and draw the letters on the blocks in the image for each stack.  Just ran out of time. 
•  A "Hint" button could reveal a different letter of the solution for each click.  
• I wonder about the "extreme" configurations.
  • Could a puzzle be created with no matching and no reversed pairs?  If not, what is the minimum sum of "In order" and "Reversed" pair counts?
  •  If the four stacks were not scrambled at all, there would be 5 pairs  in order for each stack (20 in total).  If the stacks were all inverted versions of the solution stack, there would be 5 reversed pairs for each.  Could the sum of the "In order" and "Reversed" counts be 20 for any other configurations?  If not, what is the next highest count possible?
  • My Create button filters out all non-unique random puzzles it creates, but I wonder: What is the maximum number of solutions that might exists for a particular puzzle?