I teach quite a few fun mental challenges over in the Mental Gym.

While I teach methods in as simple and straightforward a manner as possible, there isn't always just one approach. In this post, I'll take a look at new approaches to feats in the Mental Gym.

In my tutorial on Squaring 2-Digit Numbers Mentally, I already teach two methods - a mathematical approach, and Jim Wilder's pure memory approach.

NumberSense's approach takes advantage of an algebraic pattern. The number is separated into 2 variables, a being the 10s digit and b being the 1s digit. The problem then becomes (a + b)², whose expanded form shows how to make the problem easier:



Besides making the squaring of two digit numbers easier, this video also illustrates a good point about algebra. Algebra lets you see patterns of which you may not have been previously aware, and help you see a shorter, and possibly better approach.

Another mathematical challenge I tried to simplify over in the Mental Gym was the unit circle and its associated trigonometric functions.

These lessons are especially handy for students taking trigonometry. Here's a handy approach to memorizing the unit circle, especially useful for tests, that works solely by taking advantage of several simple patterns:



We'll wind up this post by focusing on two of the puzzles.

First, there's the Sudoku. I already link to instructions on Sudoku strategy, but if you find those hard to understand, e-How has a series of excellent instructional videos on the Sudoku-solving techniques that you may find helpful.

In the Towers of Hanoi, the seemingly-simple task of moving disks from 1 peg to another quickly gets complicated. Here's a short, direct tutorial that helps make the solving pattern much clearer:



If you've come across an alternative way of doing any of the feats over in the Mental Gym, I'd love to hear about it in the comments!