Monthly Archives: March 2010

John Graham-Cumming: Squaring two digit numbers in your head

Squaring two digit numbers in your head

All my life I’ve done mental arithmetic the ‘wrong way’: I’ve calculated from left-to-right, instead of right-to-left. So when I do something like 24 + 35 I’ll see the 50 first and then the 9. This even applies when there’s a carry and I’ll do something like 36 + 56 as 80 + 12. I do the same thing for multiplication as well.

Turns out I’m not so weird after all (well, apart from the finding doing mental arithmetic fun bit). I’ve been reading Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Mental Math Tricks and the author, Michael Shermer, is just like me: he works from left-to-right.

He, like me, has found this to be a good system because it lets you discard digits early and not hold some enormous calculation in your head. For example, in the calculation 124 + 353 you can immediately say “four hundred” before doing the rest of the sum. This seems to free up headspace (at least for me) and let’s me do the rest of the calculation. I’d do it like this: 124 + 353 = 400 + 24 + 53 = 400 + 70 + 4 + 3 = 477.

The books is filled with tricks for doing all sorts of mental calculations, including a nice section about estimation (I’ve always been an estimator) and working out things like tips and sales taxes. But the most fun part to me was a trick to let you do two-digit squares in your head really, really fast.

Quick, what’s 272. Of course, the brute force way to do that is to calculate 27 x 27 which is a bit of a pain because it involves doing something like 27 x 20 + 27 x 7 = 540 + 189 = 729. But there’s a much faster way.

Observe that 272 = 30 x 24 + 32. Since you probably know that 32 = 9 this means you have to calculate 30 x 24 + 9 which is relatively easy because the multiplication involves a multiple of ten which means it’s really 3 x 24 and then add a zero.

So the rule is that if you want to square number X you first round it to the nearest multiple of 10, called that X + r, and then calculate X - r (i.e. round the same amount in the opposite direction). You calculate (X + r) x (X - r) and add back the square of the amount you rounded by, r2, which will be 1, 4, 9, 16 or 25.

This works because ( X + r ) x ( X - r ) + r2 = X2 - rX + rX - r2 + r2 = X2.

Example: 672 is 70 x 64 + 32 which is fairly easy to do in your head. And naturally the same trick works no matter how many digits you have, it’s just that the multiplication gets harder.

The trick is especially impressive/easy with numbers near 100 because the multiplication becomes dead easy. For example, 962 is 100 x 92 + 42 which you (or at least I) can almost instantly see is 9216.

via jgc.org

How to extend the life of your Razor Blade keeping it sharp for months and months

via instructables.com

This video shows a simple method of extending the life of an ordinary disposable razor blade for months and months and months. Razor blades are very expensive and most people use the blade for a week or more until it gets dull, then you change it to a new one. By using this simple ‘Blue Jean Sharpening Method’ it will extend your blade life and receive a sharp and smooth shave for months and months.. I don’t know how long it will work as I am still using a blade that is at least 6 mos old now and I’m still using it…

When you finish shaving… walk to your closet… pull out one leg of a pair of blue jeans… hold the end with one hand and with the other simply stoke the razor along the entire length of the blue jean for 10 to 20 strokes… I like 20… then switch directions… the threads of the jeans run in a diagonal so switching directions allows for an balanced approach to fine tuning the blade’s edge.

This is similar to using a straight blade on a leather strap… this is cheap or free considering you have a pair of jeans!

It will take the fine nicks out of the blade and allow for you to keep the blade very sharp.

I also sharpen the blade 20 strokes before and after each shave just for good measure.

I also blow on the blade to knock off any water droplets as oxidation/rust is the biggest enemy of a sharp razor blade.

If you want, you can drop your razor ‘blade down’ into a cup of rubbing alcohol to store it until next use to eliminate any traces of water.

This should save you tons of money… at the time of this video Gillete Fusion 4 blade pack sales for $13.99 + tax. if you generally get one week’s worth of use per blade this will run you $167.88 per year + tax! If you get 6 mos per blade then you can extend your use for two years. The math works out to $7.50 per year + tax (two blades at $3.50 per ea)

Hope you get lots of shaves for free!

You Look Like I Need a Drink: How to Fold a Mattress Cover (for the XY’s)

How to Fold a Mattress Cover (for the XY’s)

Sunday, April 09, 2006

As a guy, folding my mattress cover after laundry day was quite a chore. With the corners and flaps sticking out, I used to just roll the mattress cover up under my arm in a ball and that was that. Today, I will share with you other clueless mattress folders how it can be done easily and quickly.
Step 1: Lay your mattress cover flat and pinch the corners until you have a rectangular shape. The mattress cover should resemble some odd looking elongated donut.

Step 2: Bring your pinched corners together but do not line them up.

Step 3: Here is the tricky part. With the pinched corners next to each other, take the bottom corner and slide it under the pouch of the top corner.

Step 4: If you have followed the instructions so far, your mattress cover should look something like this. If it looks slightly sloppy, do not fear, for we still have a few more steps and in the end you will have bragging rights.

Step 5: Now fold as you would normally fold. Those sneaky mattress cover flaps don’t stand a chance.

via chalkline.blogspot.com