# Hang in There! Why Even Algebraic Structures are Useful

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?

# 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 into 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.

# 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.