Since I've changed my posting schedule, I seem to have neglected my monthly snippet posts!

Not to worry, however, as we're kicking off September with a good round-up of different takes on some of my favorite mental feats.

• One of the longest-standing tutorials on Grey Matters is the classic Knight's Tour. The traditional version usually happens on an 8 by 8 chessboard. What about other irregular, non-rectangular shapes?

Over at the Wolfram Blog, Jon McLoone explored that question using Mathematica in his post Solving the Knight’s Tour on and off the Chess Board. If you're interested in the programming and the math, there's plenty in this article. Even if you don't care for all the math and programming, the variety of boards with successful Knight's Tours is amazing and amusing. Who knew Pac-Man could play the Knight's Tour so well?

• Over in the Mental Gym, I have a full tutorial on squaring 2-digit numbers in your head. I've often wanted to move on to squaring 3-digit numbers, but never really found a method that suited me. However, I recently ran across a video tutorial from Mind Math called Mental Math Trick to Square 3-digit Numbers for Faster Calculation. It breaks the problem up into 2 steps, working with the hundreds digit followed by the remaining 2 digits as a group. If you're used to squaring 2-digit numbers, this method isn't difficult to learn and adapt:



• Back in March, I wrote a post about calculating powers of e in your head. At the time, I was unaware of Colin Beveridge's post, Secrets of the Mathematical Ninja: Estimating Powers of e, which featured a quicker, yet less accurate estimate.

After seeing my post, Colin took it upon himself to develop an improved method, which he posted as Powers of e Revisited: Secrets of the Mathematical Ninja. When you're done exploring those posts, check out the rest of Colin's Blog!

• Another favorite blog topic of mine is calendars. Beyond the standard day of the week for any date feat, there's plenty of interesting mathematical patterns and shortcuts waiting to be discovered in the calendar. One of the best round-ups I've found on the internet is P.K. Srinivasan's Number Fun with A Calendar (PDF version). Besides the PDF version, there's a zipped .DOC version and even a video demonstration of some of the topics from the book:



That's all for this month. I hope you found these enjoyable and useful!