I recently stumbled upon a type of game that is not uncommon here in Germany. It is called a Scramble Squares puzzle (in German “Legespiel”). One of the most popular ones is called Knifflidiffels by Diddl. Similar pictures have to be put together. The different versions involving the cute mouse are not only very suitable for beginners, but also introduce another interesting aspect: duplicate cards.
Knifflidiffels is another Scramble Squares puzzle roughly similar to the one introduced in the article Backtracking in The Nursery. There are 5 different versions of this game. In this article, we will concentrate on the 5th version (according to the enumeration on juliesdiddlsamling.dk).
The game consists of 9 cards (see Fig. 1). This time, the pictures that have to be put together are identical (i.e. not upper and lower part of the body, as used in Pippi Langstrumpf Absolut knifflig!, but identical pictures on both sides). It is also striking that some cards are identical, namely: the first three cards (top row), cards 4 to 6 (second row) and cards 8 and 9 (second and third card in row three). Only card 7 (first card in row three) is unique. Figure 2 shows the 4 different cards of the game.
Side note: If a manufacturer wanted to print all 4 pictures (i.e. the horse, the two mice and the little dog) on every card, as it is the case here, then only a maximum number of 6 (= 4! : 4) unique ones would be possible, because cards that are just rotations of others (4 different 90°-rotations for each card are possible) are not unique. In our case, only two more unique cards are possible: Diddlina (pink skirt) would be on the top and the horse on the bottom on these cards.
Equal or Not Equal
… that is the question, when it comes to the solutions of Knifflidiffels. Using any solution as a starting point you can generate 72 (= 3! · 3! · 2!) solutions by simply swapping identical cards. Because these solutions all look the same, we will regard them as similar, too. The same holds for solutions that are created by rotating the whole playing field (see The Solutions of Backtracking in The Nursery). With these requirements in mind we arrive at 26 original solutions:
If you took into account all solutions that can be generated by swapping identical cards, there would be 1,872 solutions (factor 72). If you also took into account the solutions that are created by rotating the whole playing field, you would arrive at a total number of 7,488 (another factor of 4) solutions. A player looking for any solution of Knifflidiffels will usually be successful far quicker than if he played Absolut Knifflig! because the latter only has 148 solutions, and therefore, approximately 50 times fewer solutions than Knifflidiffels.
Legespiel-Solver Dealing with Duplicate Cards
The Java program Legespiel-Solver is free software and published under the permissive MIT License. The complete Eclipse project can be downloaded at Github. In order to display all results using the generated HTML files, you will need the 9 pictures of the cards (see the first figure of this post) . These pictures are not part of the software package, as they are copyrighted material. Starting with version v0.4, duplicate cards are handled as described in this article.
I Got No Cards
I limited this article to one version of Knifflidiffels because I simply do not have all pictures of the other versions. To make things worse, the company Depesche stopped marketing them in 2014 and my kids already took the few cards I did have. So if anyone has any left-over cards – please send them to me.