# What's New -  January 2012

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January 11, 2012: Robot Rooms implements an algorithm for exactly covering a rectangular area with random rectangles meeting certain size and shape constraints.  Earlier exact covering algorithms tended to generate many long and skinny rectangles or with a large range of sizes. Neither of those properties are  desired if we want to design dungeons or  rooms for robots to explore!.

January 12, 2012: Logic Solver  a program that can help solve many logic problems commonly found in puzzle magazines and books.  Here is a simple example:

Mary, John and Pete have red, brown, and blonde hair, and are 13, 14, and 15 years old .  Using the following clues determine the hair color, and age of each child.
1. The youngest has blonde hair.
2. John is older than Pete.
3. John does not have red hair and Pete does not have blonde hair.

From these facts the program can apply rules of logic to match the children up with their ages and hair color.  Previous versions would handle up to 100 facts; Logic Solver Version 3.3 posted the other day solves problems at least twice as large as the  previous version.   Click the link to see the rest of the story.

January 18, 2012:

 X, Y Data 1.1,  2.1 2.3,  3.9 3.7,  6.1 3.9,  7.9 4.0,  9.0 5.0,  11.0 Best Fit Line is Y=2.3X-1.0,               R2=0.9384

A Delphi programmer  recently requested information about determining the slope of the regression line through a set of (X, Y) data points.  It seemed like something I must have written and posted in the 11 years the site has been around but that doesn't seem to be the case.  So here is LinearLeastSquares which takes a set of points, plots them and draws the "best fit" regression line.  It also displays the equation of the line and Correlation Coefficient, R (actually R2, called the  Coefficient of Determination) indicating how well the data are linearly related.

January 27, 2012:  Here are a couple of interesting probability problems solved analytically (describing the logic leading to the solution) and experimentally (running a million trials of a simulation model),    Fifty Probability Problems presents  two problems  about ladder tournaments.  Plans are to add more of the 50 in the future.