**Hardly any other subject can hit a freshman as hard as those strange “algebraic structures” during your first math course. You started out to solve real problems and now this professor explains to you, with a straight face, that there really exists such a thing as addition and multiplication and that surprisingly 0 is not equal to 1. What’s that got to do with the world?**

# Author Archives: Andreas Keilhauer

# List of Scramble Squares Puzzles with solutions

**This list covers variations of a certain kind of tile based games called Scramble Squares (in German: “Legespiel”) in which square cards must be placed to form a larger square so that the images of all cards fit together at the edges. It shows the number of solutions and what they look like exactly. All solutions were calculated with the software Legespiel-Solver. The results also make it possible to estimate how difficult the respective Scramble Squares puzzle really is.**

# New Home for Gravisto

**Gravisto (Graph Visualization Toolkit) is a program for visualizing and editing graphs. Over the course of 15 years, many useful plugins have been developed to handle graphical information efficiently. Unfortunately, this open source project had recently become homeless and needed a new home.**

# Getting Hierarchical Information into Shape

**Family trees, organizational charts, taxonomies or product breakdown structures can be very large. That is why compact and clear drawings of hierarchical information are important. But space requirements vary depending on the individual use case. TreeJuggler can optimize drawings for any aspect ratio. This will be demonstrated in a short video.**

# TreeJuggler-Tutorial – Tree Juggling For Beginners

**Drawing complex hierarchical information manually is both cumbersome and time consuming. This task should not be done manually, but with a suitable piece of software. TreeJuggler is such a tool. It can layout hierarchical information compactly and optimize the drawing for any aspect ratio you need. Here is how to use it…**

# Problem Reduction – The Most Reliable Path is Just Another Shortest Path

**Applications like Google Maps or navigation systems calculate shortest paths or fastest paths all the time. There have been very efficient algorithms to solve this task since the 50s. The most reliable path can be found via the same methods – using a little trick.**

# Solving Knifflidiffels – Scramble Squares With Duplicate Cards

**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.**

# Juggling with Trees – How to Layout Hierarchical Information Compactly

**Hierarchical information is everywhere: Family trees, organizational charts, taxonomies or product breakdown structures. A good graphical representation can convey a lot of information very quickly. However, creating such a drawing manually is cumbersome. This article will show how such a task can be performed automatically.**

# Rounding Errors And Arbitrary Precision Arithmetic

**The computer computes. Plus, minus, times and sometimes even divide. The results are always correct. Really? Computers usually use floating point numbers, which are very flexible, but still can cause quite substantial rounding errors – at least when you are doing complex calculations with many steps. These small inaccuracies can accumulate and become a creeping poison. Arbitrary precision arithmetic offers a way out.**

# Backtracking in The Nursery – How to Solve Scramble Squares

**I recently stumbled upon a game that is not uncommon here in Germany. It is called Scramble Squares (in German “Legespiel”). The specific type of tile-based game, this post will be about, has quadratic cards with pictures on them. These pictures must be arranged to a square in such a way that the pictures on each card fit together with the pictures of the cards around it. I will show how complex this problem is and also present an algorithm to solve it.**