## Saturday, March 26, 2011

### How And Why Does Osculation Work In Divisibility Tests?

As explained in earlier posts, osculation is the process of multiplying the last one or more digits of a number by some constant and adding the result to the left-over part of the number (positive osculation) or subtracting the result from the left-over part of the number (negative osculation). If the osculation involves just the last digit of the original number, it is called simple osculation. If the osculation involves more than one digit, it is called multiplex osculation. We also saw in the post on divisibility tests how to use osculation in divisibility tests for numbers like 7, 13, etc., even though we did not, at that time, know that we were using osculation.

The question naturally arises as to why or how osculation works in determining divisibility. In this post, I will look at the mathematics of how osculation enables us to test for divisibility. To start on this path, we need to understand the concept and properties of a mathematical operator known as the modulus operator. Most of us are probably already familiar with this operator, but we will use the first part of this post to re-examine the modulus operator, and then we will look at its relationship to osculation.

The modulus operator, to put it in simple terms, gives us the remainder of the division of the first operand by the second operand. It is usually denoted by the term “mod” between the first and second operands (in many programming languages, the modulus operator is implemented as a function that takes the two operands as arguments). Usually, the result of the modulus operator is defined only when the second operand is positive. Some examples of the results from the modulus operator are given below.

• 25 mod 5 = 0
• 26 mod 4 = 2
• 31 mod 2 = 1
• 12568 mod 11 = 5
• 3 mod 28 = 3
• 7 mod 7 = 0
• -31 mod 6 = 5 (-36 is the highest multiple of 6 below –31, and the difference between –36 and –31 is 5)

Here are some properties of the modulus operator that we can readily derive from its definition. We will restrict ourselves to the use of the modulus operator when the second operand is positive.

• The results of the modulus operator can range from 0 to n – 1, where n is the value of the second operand
• x mod y = x when x < y
• x mod y = 0 when x = y
• if x mod y = 0, then x is divisible by y
• if x mod y = 0, then ax mod y is also 0, where a is any constant. This means that if y is a factor of x, then y, by necessity, has to be a factor of ax also
• But the reverse is not true: thus if ax mod y = 0, that does not mean that x mod y = 0. As an example, 2*4 mod 8 = 0, but 4 mod 8 is not equal to 0
• In general, if a and y are not co-prime, then it is possible for ax mod y to be 0 while x mod y is not. If a and y are co-prime, then if ax mod y = 0, then x mod y = 0
• Regardless of the value of x mod y, yx mod y is always 0 (multiplying the first operand by the second operand makes the second operand a factor of the product)
• if x mod y = a, and z mod y = b, then (x + z) mod y = (a + b) mod y
• x mod y = (x + ay) mod y (this follows directly from the previous property since ay mod y is always 0)
• if x mod y = a, and z mod y = b, then (x – z) mod y = (a – b) mod y
• the previous rule then leads directly to this one: x mod y = (x – ay) mod y
• x mod y + (-x) mod y = y if x is not divisible by y
• x mod y + (-x) mod y = 0 if x is divisible by y. Combined with the third rule above, this implies that (-x) mod y is also equal to 0 if x is divisible by y

Now, let us look at a divisibility rule that uses osculation, in the context of the properties above to try and understand how it works. One of the simplest such rules is that if the positive osculation of a number by 5 is divisible by 7, then the original number is divisible by 7. Thus, for instance, 364 is divisible by 7 because 36 + 5*4 = 56, which is divisible by 7.

To understand why this works, let us first break the given number into two parts. The first part will take into account all the digits except the last digit, and the second part will take into account the last digit. Thus, 364 = 36*10 + 4. In general, any number with more than one digit can be rewritten as 10x + y, where x and y are non-negative integers.

What does the number (10 x + y) being divisible by 7 mean?

It means that (10x + y) mod 7 = 0.

Since x mod y = 0 implies that ax mod y = 0, let us multiply the first operand by 5 (note that 5 and 7 are co-primes, so 5x mod 7 = 0 implies also that x mod 7 = 0). We get 5*(10x + y) mod 7 = 0.

Expanding this out, we can then say that (50x + 5y) mod 7 = 0.

Now, recognizing that 49x is a multiple of 7 (since 49 is divisible by 7, and x is some non-negative integer), we can subtract 49x from the first operand without affecting the result of the modulus operator. Thus, (x + 5y) mod 7 = 0.

But, that is precisely what the divisibility rule says. Recognize that x + 5y is the positive osculation of (10x + y) by 5. Thus, step by step, we have derived the positive osculation divisibility rule for 7.

We can do the same thing for the negative osculation test for divisibility by 7 also. Remember that the test says that if the negative osculation of a number by 2 is divisible by 7, then the number is divisible by 7. Thus, in the case of 364, it is divisible by 7 because 36 – 2*4 = 28 is divisible by 7.

Once again, consider the given number to be 10x + y. 10x + y being divisible by 7 implies that (10x + y) mod 7 = 0.

Multiply the first operand by 2. This gives us (20x + 2y) mod 7 = 0 (once again, note that since 2 and 7 are co-prime, 2x mod 7 = 0 implies that x mod 7 = 0).

Recognize that 21x is a multiple of 7 because 21 is divisible by 7 and x is a non-negative integer. We can then subtract 21x from the first operand without affecting the result of the modulus operator. This gives us (-x + 2y) mod 7 = 0.

Since x mod y = (-x) mod y when x is a multiple of y, we can multiply the first operand by –1 to get (x – 2y) mod 7 = 0.

Thus, (x – 2y) mod 7 = 0 implies that (10x + y) mod 7 = 0. This proves the negative osculation divisibility test for 7.

As you can guess at this point, the practitioners of Vedic Mathematics simply codified all this into the concept of natural osculators or vestanas. It is easy to identify multiples of a number that end in 9 or 1 like we did above for 7 (49 and 21) so that we can reduce the 10x in (10x + y) to just x by subtracting the multiple of the number that ends in 9 or 1.

But, now that we know the secret behind osculation and its use of the properties of the modulus operator to test for divisibility, we can derive our own divisibility tests without any problems. And some of them could be much better or more convenient to use than the tests we learned about in the post on divisibility rules.

For example, let us put to good use the facts that 1001 is a multiple of 7, and any number can be expressed as 1000x + y (with non-negative x and y). Obviously, this works best when the number is at least 4 digits long.

(1000x + y) mod 7 = 0 implies that (-x + y) mod 7 = 0 (we simply subtracted 1001*x, which is a multiple of 7 from the first operand).

This then tells us that (x – y) mod 7 = 0.

Let us test this out on 27,118. In this case, x = 27 and y = 118. x – y = –91, which is divisible by 7. We can verify that 27118 is also divisible by 7. We just derived another divisibility rule for 7! This divisibility rule uses multiplex osculation rather than simple osculation.

Similarly, 1001 is a multiple of 13 too. So, we can say that if the number can be expressed as 1000x + y, and x – y is divisible by 13, then the number is divisible by 13. Take the number 50,037, for instance. Since 50 – 37 = 13 is divisible by 13, we can say that 50,037 is divisible by 13. It is easy to verify that this is indeed the case. With very little effort, we have derived another divisibility rule for 13 based on multiplex osculation!

Obviously, having a multiple that is one away from a power of 10 makes this convenient, but the principle works even if that is not the case. For instance, 1003 is a multiple of 17. Thus, if a number can be expressed as 1000x + y, then (1000x + y) mod 17 = 0 implies that (–3x + y) mod 17 = 0 (we just subtracted 1003x, which is a multiple of 17 from the first operand). The result is not a divisibility rule based on osculation, but might be just as convenient to use.

For instance, take the number 83,215. In this case, x = 83 and y = 215. y – 3x = 215 – 249 = –34. Since –34 is divisible by 17, we can conclude that 83,215 is also divisible by 17. It is easy to verify that this is indeed true.

992 is a multiple of 31. Using that fact, we can derive the divisibility rule that if the number can be expressed as (1000x + y), then if (8x + y) is divisible by 31, then the original number is divisible by 31 too. Thus 3007 is divisible by 31 because x = 3 and y = 7, and 8x + y = 24 + 7 = 31, which is obviously divisible by 31.

Now that we have unraveled the secrets of osculation and how the combination of osculation and the modulus operator results in divisibility tests, we can all go wild deriving dozens of divisibility tests for any number we are interested in. You might discover divisibility rules that are much easier to apply or appeal to you for some other reason. All you have to do is find a multiple of the divisor that is in the vicinity of a power of 10, and you are all set! Try a few. I am sure you will be hooked on it. Discovery is a powerful and addictive feeling!!

## Friday, March 18, 2011

### The Dell Inspiron 15R Definitely Fits The Bill For Me

As mentioned in this previous post, I picked up a Dell Inspiron 15R laptop over the President’s Day weekend last month. I was getting a little tired of juggling my vast digital horde of photographs, videos, ebooks, etc. on the 250 GB hard drive of my previous laptop, a Dell Vostro 1500. I managed for a while by buying an external hard drive, but eventually, I decided not to put up with it anymore. What pushed me over the top was a sale at Dell that brought this Inspiron 15R laptop down to a very decent price of just \$450. My budget for a replacement laptop was \$500, so when I got something decent for less than that, I decided it was not worth putting the purchase off. I probably will not see prices this low for equivalent hardware till near the end of the year.

By the way, the Dell Vostro 1500 is one of the best laptops I have ever purchased. It is a rock-solid computer that withstood all the abuse I threw at it and never once quit on me. It runs cool and quiet, and even though it is now over 3 years old, its battery lasts a full 6 hours when I do light web-surfing and music-listening on it (the battery is a 9-cell battery that used to last for just over 7 hours when it was new). It has a solid feel to it, and I love its screen quality, brightness and colors. And I paid about the same for it as I ended up paying for its replacement. My only problem with it, and the only reason I had to get a replacement computer was the lack of hard disk space on it. I considered replacing its hard disk, but the economics of it simply did not make sense to me.

The Inspiron 15R is obviously available from Dell, where you can customize it with different colors, play around with hard disk sizes, amount of RAM, etc. It is also available at online retailers like Amazon.com, but usually only in some base configuration without much ability for you to customize it. The configuration I got it in is not available at either Dell or Amazon right now, but you can get a 15R with a slightly faster processor than I got for \$550 from Dell. By the way, even though the laptop is marketed as an Inspiron 15R, the official model number for the laptop is the Inspiron N5010. If you want drivers or other downloads for the laptop from the Dell website, you can’t find a product called the Inspiron 15R on the support side of the Dell website. There, the model is only referred to as an Inspiron N5010.

Let me start with the specifications of the laptop on which I am writing this review:

• Intel Core i3 370M processor running at 2.4GHz
• Windows Home Premium 64-bit operating system
• Glossy 15.6 inch LED-backlit LCD display with 1366x768 native resolution, capable of 720P display
• 4GB of DDR3 RAM running at 1333 MHz
• 500 GB hard drive running at 5400 RPM
• 8X CD/DVD Burner (Dual Layer DVD+/-R Drive) with Roxio Burn
• Intel Centrino Wireless-N 1000, 802.11 b/g/n
• Bluetooth
• 6-cell lithium-ion battery, rated to last just over 4 hours
• Integrated 1.3MP webcam and microphone
• Intel HD Graphics
• 7-in-1 media card reader (SD, SDHC, SDHD, MMC, MS, MS Pro, xD)
• Built-in stereo speakers with 4W of total power
• 3 standard USB ports
• 1 USB/e-SATA combination port
• HDMI and VGA output ports
• Ethernet port
• 1 microphone and 1 headphone port
• 14.7” x 9.6” in width and height
• 1.02” to 1.48” inches in thickness (when closed), with the back thicker than the front
• 5.8 lb weight including the battery, not including the power cord

The laptop arrived within 3 days of placing the order with Dell (free 2-day shipping was included in the sale, saving me about \$50 more). In the package was the laptop itself, the laptop battery, the power cord and the instruction manual. There were no media disks or system recovery disks of any sort included. Unpacking and setting up the computer was trivial, as is to be expected.

The power cord is significantly different from the power cord that came with my Dell Vostro 1500. The adapter is still rated for 65W, and the tips are interchangeable (so my old laptop can be powered by the new power cord and vice versa with no problems), but the brick itself is much lighter and smaller than before. Moreover, the cord that goes from the brick to the wall outlet does not use the funky Dell 90-degree turn connector anymore. Instead, it is a regular straight connection that makes the entire power cord much better to look at. The adapter can take 100-240V, 50-60Hz AC power as input, so it should be possible to use it without the need for any transformer of any sort, pretty much throughout the world.

The casing of the computer is a greyish-black that Dell refers to as Mars-black. It is very smooth and shiny, and smudges easily. The screen is slightly smaller than the base of the laptop, so the screen hinges are located about an inch inside the base, and the last one inch of the base protrudes behind the screen. Whether it is open or closed, the laptop looks sleek and stylish. The screen is pretty much the same thickness throughout, with the base being significantly thinner in the front and thicker in the back. The laptop screen does not have any latches that keep it closed on top of the base, instead like all modern laptops, the hinges are designed to keep the lid closed when they are closed by the user. This also means that it is hard to open the laptop with a single hand (which is not a problem at all with my Vostro 1500).

The webcam is on top of the screen, and includes a small LED light next to it that serves a dual purpose: it tells you when the webcam is on, and it provides a little light to make the webcam image slightly better-lit. The microphone is located in the middle of the base at the front of the computer. The speakers are located on either side of the base at the front of the computer rather than being right next to the screen. Since the front of the base curves backwards, the placement of the speakers and the microphone is a little unintuitive since it feels as if they face the surface on which the laptop is placed rather than facing up and at the person sitting in front of the laptop.

The power button is located on the top left corner of the base. The base consists of a full keyboard, including a separate numeric keypad. Below the keyboard, approximately centered with respect to the space bar is the touchpad. The touchpad is clearly demarcated from the surrounding area, being slightly depressed below the level of the wrist rest, and being completely back instead of the chrome that surrounds the entire keyboard. The touchpad keys are chrome-colored.

The keyboard does not have chiclet keys that seem to be in vogue now. They are regular keys that are fine to type on. They appeared less solid than on my Vostro 1500, but I have banged away on them for the past month or so, and they have held up fine so far. The numeric keypad can be used for entering numbers when the numlock setting is on, and are used as arrow keys at other times. There are no arrow key markings on these keys, but I have used them as arrow keys and they do work (4 is left, 6 is right, 2 is down, 8 is up, 7 is Home, 1 is End, 9 is PgUp and 3 is PgDn). The dedicated arrow keys on the keyboard are half-height, so it takes some getting used to to use them accurately.

The row of function keys on the top row of the keyboard are dual-purpose keys that also control things like volume, screen brightness, media playback, etc. You have to press the Fn key on the keyboard to activate the function keys, otherwise by default they function in their alternate roles. You can change this behavior in the BIOS, or you can change them using a software application called Dell Quickset that comes with the computer. Most of the actions of these keys have an onscreen confirmation. In addition, the Caps Lock and Num Lock buttons create icons in the taskbar of Windows 7 that look like a capital “A”, and a “9” (white letters on a black background) respectively. These taskbar icons do not have infotips, and they don’t respond to mouse-clicks, right-clicks or double-clicks. It took me a while to figure out what they meant. Why Dell would write software to put these icons on the taskbar, but not even provide them infotips is beyond me! There is no Scroll Lock button on the keyboard.

On the back of the computer are the power inlet, two USB ports and the VGA port. On the left hand side of the computer are another USB port, air vents, the headphone and microphone ports and the HDMI port. On the right hand side of the computer are the ethernet port, the USB/e-SATA combination port, the optical drive and the card reader. On the front of the computer, on the left hand side are three indicator lights. One of them indicates power status, the second indicates hard drive access and the third one shows battery charge status. The meaning of the different light indications on these lights is explained in the user manual that comes with the computer.

The user manual is somewhat detailed, but is not really detailed. It is better than the manual that came with the Lenovo computer I reviewed earlier, but it is not in the same league as the thick manuals that came with my Vostro 1500 3 years back. The manual does have details about how to create recovery disks, how to use the recovery partition or the recovery disks to repair the operating system if necessary, etc.

Once you install the battery and plug the adapter in, you are ready to switch on the computer and set it up. The hard disk installed in the computer is a Seagate disk, model number ST9500325AS. It is partitioned into 3 partitions: a 100 MB partition labeled “OEM partition”, a 15 GB recovery partition, and a 451 GB partition that is for your use. The total size is approximately 466 GB, which is how a disk advertised as 500 GB will appear to the operating system (see here for an explanation of this shrinkage).

After I activated Windows 7 and created user accounts and what not, it was time to clean out the hard disk. It came loaded with a lot more junkware than other computers I have set up recently. The junk consisted of programs and trialware from various software vendors, and took me over 3 hours to identify and clean out. After that, I loaded the computer with my preferred software. I then transferred over all my files from the old computer using an external hard drive. It took me several more days to set the computer up just the way I like it, but the computer was useable within a day.

In terms of performance, the combination of the dual-core hyperthreading CPU (which essentially allows the computer to behave as if it has 4 independent processors) and the 4 GB of RAM make for a very high-performance computer. The lack of dedicated video hardware would probably make this laptop less than optimal for heavy-duty gaming, but this computer is more than adequate for all my needs. The computer opens documents and spreadsheets with blazing speed, and plays back video and audio files smoothly and without any glitches.

Unfortunately, in spite of the large amount of junkware on the computer, it did not come with any software dedicated to DVD playback. The computer comes with Windows Media Center, a monster of a program that seems to have more bugs than features. It crashed repeatedly when I played DVD’s using it, and even blue-screened my computer a couple of times. Eventually, I got sick and tired of it, and started using VLC to play DVD’s. But the lack of dedicated DVD playback software on the computer was disappointing.

The computer also comes with Dell software that allows one to make a system recovery disk that is capable of resetting the computer to factory state if needed. You can do it using the recovery partition on the hard drive anyways, but if you lose that partition because of hard drive failure, or if you decide to upgrade to a different hard drive, you can use the bootable media created by this software (called Dell Datasafe) to get the computer back up and running in short order. You need either a USB stick with at least 8 GB capacity or a dual-layer DVD to record the recovery media.

Unfortunately, the software did not work as advertised for a couple of weeks, preventing me from creating a recovery disk. The program kept complaining that I would need to reboot the computer at least once before it could create recovery media, but the message wouldn’t go away however many times I rebooted the computer. Finally, the message went away by itself one fine day, and I was able to create a bootable recovery image on a 16 GB USB stick.

The battery is decent, but obviously not as good as advertised by Dell. It easily lasts a little over 3 hours under mild use (web-surfing, listening to music, etc.), but not for 4 hours as claimed. The laptop includes an innovative feature that allows you to disable charging of the battery when the laptop is powered using the power cord. Some people claim that keeping the lithium-ion battery charged to between 40 and 60%, instead of keeping it charged up to a 100% (and continuing to charge it) is better for the health of the battery. This laptop gives you the ability to do that if you subscribe to that theory. However, one annoyance I have encountered with the computer is that the display blanks out completely for about a second whenever you switch from AC power to battery or vice versa. I have no idea why, and this is the first laptop I have seen that does this. Very weird, but nothing more than an inconvenience though (only the display is affected, not the programs running on the computer).

Apart from these annoyances, the computer has been just about perfect so far. The screen is very bright and absolutely gorgeous. The keyboard is responsive and easy to use. The touchpad is an absolute pleasure to use, and is multi-touch capable (thus allowing for zooming, rotating, scrolling and going back and forward on a web browser using multi-finger gestures). The computer runs very cool, and the fan hardly ever comes on. When it does, it is very quiet, and it is easier to feel the hot air coming out of the vent with your hands than it is to hear it with your ears. The wi-fi connects reliably and speedily. The speakers are quite loud, and even though they are not right below the screen, facing upwards from the base, they are easy to hear. I did not get a chance to test out the microphone.

So, here are my opinions about the laptop.

The good:

• Fast processor, abundant RAM, generous hard disk size
• Gorgeous screen with good brightness and contrast
• Lots of USB ports, on all sides of the computer
• e-SATA port, and 7-in-1 card reader
• Bluetooth enabled (though I never tried out the bluetooth since I don’t have any bluetooth accessories to test it with)
• High resolution webcam, built-in microphone
• Good keyboard, excellent touchpad
• Sleek, stylish looks
• Decent documentation. In addition to the user manual, you can also download service manuals from the Dell website. Just remember to look for documentation for Inspiron N5010’s, not for Inspiron 15R’s
• HDMI output for connecting the laptop to your HDTV
• Ability to keep the battery in the laptop without having to charge it to 100%
• Power supply compatible with (some) previous models from Dell

The annoying:

• Creating recovery disks is a hit-or-miss process because of poorly designed Dell software
• The screen goes completely dark for a second every time I change power sources
• The cover-plate of the optical disk is large and reaches all the way to the bottom of the laptop, and sometimes opening the DVD tray can be difficult if the computer is on a soft or uneven surface, like on a bed for instance
• The microphone and speakers sort of face downwards rather than up towards the user
• No dedicated hardware buttons for controlling volume, screen brightness or media playback
• The case and screen attract smudges and fingerprints

• Large amount of junkware on the computer, requiring lots of effort to get rid of
• No dedicated DVD playback software included
• No recovery disks provided with laptop though (unreliable) software is included on the machine to create recovery media (how much does it really cost to package a DVD with the factory image on it? Really, is it that much cheaper to develop buggy software, install it on the computer, and field support calls about it, than to just include recovery media with the computer and be done with it?)
• No firewire (IEEE 1394) port to hook up my camcorder (yes, I know, it is high time I replaced my 10-year-old camcorder with something more contemporary, but that is another project for another time!)
• Upgrading the laptop is very difficult. Except for the RAM none of the other parts of the computer (such as the hard drive) are directly accessible from the back of the laptop. Instead, according to the service manual, replacing the hard drive, for instance, involves almost completely disassembling the laptop, taking out the keyboard, touchpad, etc.

Overall, I would rate the computer a solid 4.5 out of 5. Improvements are possible, but the computer is an excellent buy as it stands right now. It is difficult to find a computer at this price with all the features this computer has. And when it goes on sale, it is even more difficult to come anywhere close to this kind of value. I wish Dell would stop loading these machines down with junk, and make some minor improvements such as providing buyers with recovery media out of the box. But none of these problems would keep me from buying this computer since there is really nothing else on the market that comes close in terms of value for the money. If you like tinkering inside your laptops, this may not be the ideal laptop for you, though the prospect of taking it apart to get to the insides might excite you if you are a hard-core tinkerer!

## Saturday, March 12, 2011

### Review Of Snowjoe SJ620 Electric Snowblower

This is the long-delayed full review of the electric snowblower that I bought at the end of January of this year. Since then, I have been trying to write a review of it, but something or the other has always come up and prevented me from finishing up such a review. As it stands, this review may be a little late for this winter (at least in the northern hemisphere), but as they say, better late than never. Hopefully, the product will be available next winter also, and this review might come in handy at that time. You can also read this earlier post for a mini-review of the performance of this snowblower.

The SJ620 snowblower is manufactured by Snowjoe Incorporated, a New Jersey company. It is available from Amazon.com and other online retailers for around \$200. I bought mine new from VM Innovations for under \$200 (though they seem to be selling only a refurbished one right now). It came in about 2 days in an approximately 2-foot cubical box that weighed in at about 35 lbs. Unpacking the thing was quite simple. Once you get the snowblower out of the box, and rid it of its plastic coverings, you see that the thing is pretty much fully assembled.

Pretty much the only thing left for you to do is to straighten the handle (which is folded into 3), and tighten the bolts at the joints so that the handle stays straight. You also have to attach a slender rod as a handle for the chute that directs snow that is blown by the snowblower. That is pretty much it. The snowblower is now ready to use.

The assembled snowblower weighs about 31 lbs. It comes with three user manuals, one in English, one in French and one in Spanish. I threw away the ones in French and Spanish. The first part of the manual explains in detail how to assemble the snowblower (with lots of pictures). After that it explains how to hook up the electric cord, and what types of cord to use. To summarize this section, this snowblower requires 13 Amperes of current delivered to its motor. If you are going to use up to a 50-foot long extension cord, that cord can be 14-gauge. Anything between 50 and 100 feet requires 12-gauge wire. Using an inadequate gauge for the extension cord can lead to heating of the cord, overheating of the snowblower motor, poor performance because the motor does not operate at full capacity, or even fire.

The next few pages of the manual explain how to start and operate the snowblower and is filled with the usual precautions about making sure you don’t hit loose rocks and other debris. Then the manual explains how to replace the drive belt and other user-replaceable parts of the snowblower in case of failure or wear and tear. Apart from the drive belt, the rubber plates on the auger blades, and the scraper bar at the bottom of the snowblower are also user-replaceable.

Most parts of the snowblower are made of plastic. The auger blades are made of metal, but pretty much everything else is made of plastic, including the housing in which the auger operates. I opened up one of the side panels on this housing to see how the motor is linked to the auger blades, and found that the pulley over which the drive belt is wound is plastic also. You can see a picture of this plastic pulley in the picture to the left.

In preparation for the snowblower, I went to a local hardware store and got things that I know I need to use with the snowblower. Most important of these purchases was a 100-foot 12-gauge extension cord. I got a good low-temperature wire with a lighted end. The lighted end is not that important though it does come in handy by letting you know immediately if the plug end has fallen out of the wall outlet. Cords designed for use in low temperatures remain flexible at sub-freezing temperatures, making them easier to manipulate. This is particularly handy when you are dragging the wire back and forth across your driveway behind a snowblower. My extension cord cost me about \$45, and you can also get cords like these online.

Secondly, I also bought an extension cord reel that will help me keep the wire wound up and out of the way when not in use. The reel is also useful in making sure that the wire does not get damaged because of people stomping on it all the time, or by being run over by your car in the garage, etc. I got my reel for under \$10.

I also bought some spray cans of silicone lubricant. Jig-A-Loo and Liquid Wrench are the brands I bought, but any other silicone lubricants would probably work just as well. Once I finished assembling the snowblower, I sprayed a coat of silicone lubricant on the snowblower’s blades, the inside of the blade housing, the chute and the joint between the snowblower body and the chute. These are places that will come in contact with snow, and the silicone lubricant keeps the snow from sticking to these surfaces. This helps prevent clogs and freeze-ups.

Starting and operating the snowblower are are very easy. There is a large blue button on the right hand side of the handle near where the extension cord plugs in. You depress this button while pulling the trigger against the handle to start the snowblower. Let go of the trigger, and the snowblower shuts down. Once it shuts down, pulling on the trigger again will not restart it. You once again have to hold in the button while pulling on the trigger to restart the snowblower. I had no problems operating either the button or the trigger with heavily gloved hands.

The snowblower is not self-driven, so you have to push the snowblower to move it. I found that the snowblower was quite easy to push because of its light weight, but the light weight also means that you have to push down on it to make sure it cleans up snow all the way to the ground level. Otherwise, the lip will ride over a couple of inches of snow next to the ground, and end up leaving that layer of snow on the ground.

As mentioned in this post, I got a chance to use this snowblower almost as soon as I put it together. And the snowblower did an excellent job in my opinion. It did not have any problem blowing through 9 or 10 inches of snow even though that is slightly over the 8 inches the user manual mentions as the maximum height of snow this snowblower is supposed to be used on. The throwing distance was anything from 10 feet to 25 or 30 feet depending on the type of snow I was blowing. The throw distance also depended on the quantity being thrown, with the distance increasing with quantity up to a certain point and then decreasing after that. The optimal snow depth for maximal throwing distance seemed to be about 4 to 6 inches depending on the weight of the snow being thrown.

The snow blower did not have any problem with the heavy ice and water mixture left at the end of my driveway by streetplows either. The last 4 or so feet of my driveway usually take me about 45 minutes to clear with a snow shovel. Now, this snowblower clears that up in about 10 minutes. Add in about 15 to 20 minutes for the rest of the driveway, and my entire driveway is clear in about half an hour instead of the usual hour and a half to two hours I used to take, clearing the whole driveway with a snow shovel.

The only problem with the snowblower was that one of the retaining clips holding the wheel on the axle broke off at some point, leaving the axle disconnected from the bracket that holds the axle to the snowblower body. This caused the wheel on the right hand side of the snowblower to drag along the floor instead of holding up the snowblower. But this was not a huge issue since the snowblower is very light, the wheels are tiny, and the snowblower moves along quite easily whether or not that wheel is actually in place. You can see the axle popped out of the bracket in the picture to the left.

I was somewhat upset when this happened, but it is purely a mechanical problem, so I set about figuring out how to repair it myself. That is the way my engineering mind works. I actually did not know what held the axle to the bracket. Looking at the other side of the axle, I could see a black ring around the axle on the outer side of the bracket, but I did not know what it was exactly. I decided to improvise, and devised my own solution using a paper clip, which I wrapped around the axle to keep the axle from popping off the bracket. The picture to the right shows this axle held up with the paper clip.

Unfortunately, this fix lasted only a short time, and the paper clip popped off the axle during the stress and strain of pushing and pulling the snowblower across my driveway. I then went to the Snowjoe website and used their contact form to describe my problem and ask them for a solution. I waited for a couple of days, but never got a response to that submission.

So, I called up Snowjoe, and managed to get through to a live operator within 15 minutes. I explained my problem to the operator, who told me that the part that holds the bracket to the axle is called a retaining clip or circlip. He could not tell me what the diameter of the circlip needed is, but since the axle itself is exactly half an inch in diameter, and the circlip fits in a groove cut into the axle, a circlip just below half an inch in diameter (such as 3/8ths of inch or 7/16ths of an inch) would probably fit. You can find circlips of many different diameters in your local hardware store, so if this should happen when the snowblower is outside warranty, you can buy your own circlips (under 50 cents each) and fix the problem. In my case, since the snowblower was under warranty, Snowjoe arranged to send me a circlip by mail (I should have gotten it about 3 days after they mailed it, but the USPS lost that first mailing, and I had to call Snowjoe and ask them to send me a second one, so I actually got mine only about 20 days after I first called Snowjoe).

The verdict? I would rate this snowblower a solid four and a half out of 5 stars. It works as advertised, and is plenty powerful for the kinds of light snowfall it is rated for (obviously, if you live where you get 10 feet of snow every winter, you probably want, and have, something a lot bigger and more powerful). It is light and easy to operate, and held up well under pretty stressful conditions. The all-plastic construction is somewhat worrying, but that is what makes the machine light and easy to handle. The breaking of the circlip around the axle was upsetting, but Snowjoe’s customer service was very good (and that breakage gave me an opportunity to actually call and test their customer service). If your snowblowing needs are similar to mine (about 3 feet of snow a year, very seldom over 6 inches of snow at a time), you will probably not go wrong getting this snowblower.

## Wednesday, March 2, 2011

### I Have Not Been Lazy – I Have Just Been Busy. Really!

I can’t believe it has been almost 3 weeks since my last blog post. Things sometimes have a habit of piling up unexpectedly in my life, and this has been one of those weird periods when a bunch of things came together and derailed all my efforts to put more stuff up on my blog.

The most important thing that happened was that I decided that I wanted to finish cataloging my entire collection of digital books within the next few weeks. I have been involved in this activity on and off for the past year or so, and my slow pace combined with a penchant for downloading more books off the internet made it seem like I was barely staying in place. In fact, at several times of the year, the backlog was bigger than what I started the week with.

So, I put a halt to all downloading, and I have decided not to acquire any more digital books until I was done putting what I had into my database. The only way I was going to take advantage of all the digital books was if I could search and find what I wanted when I wanted it. And the only way to do that was to keep everything cataloged in my database. So, I started devoting every free minute I had to the digital book catalog. Thanks to these diligent efforts, I have entered about 500 books into my catalog in the past few weeks. I still have about 500 to 1000 left to enter, but at this rate, maybe I will be done within a month or so. After that, all I have to do is make sure I keep up with my rate of acquisition!

The second thing that happened was that I got a new computer. I was managing with my old computer and its inadequate amount of disk space by juggling stuff between the computer and external hard drives. But Dell had an excellent sale on Inspiron 15R laptops over the President’s day weekend, and I got a chance to pick up a powerful Intel Core I3-based computer with 500 GB of hard disk space for under \$450.

It was just too tempting for me to let go. I might have to wait till the end of the year to see prices like that on equivalent hardware, so I jumped on it. And after that computer was delivered, I have been busy setting the beast up. I have been used to Windows XP for the past 7 or 8 years, and this new computer came with Windows 7 64-bit. I know my way around the XP operating system and can navigate it blind, but Windows 7 threw a few curveballs at me that took some research and searching on the internet to figure out.

I like my computers set up just so. The desktop arranged in a particular way. The folders and files arranged in a particular way. A particular set of software installed and ready to use, and so on. All this takes time on a new computer. Throw in a new operating system, and the process took much longer than I expected. The new computer is finally set up and I have started using it instead of my old computer. But I am still spending time on the internet researching obscure issues that crop up (for instance, one of my file types did not have any icons associated with it. This is a simple problem to fix on Windows XP, but apparently, not so easy to fix on Windows 7 unless you use third party software or dive into the innards of the windows registry).

So, finally, I decided that it was time to take a breather, and put up an explanation for the lack of posts on my blog before plunging back into stuff that needs to get done. I still owe my readers a review of the new snowblower I bought (though, by the time I put it up, only readers in Antarctica might need it!). I also need to put up new posts on Vedic Mathematics and Microsoft Access. And I have the beginnings of a review of the new computer in my mind too. All of this will come out soon, though at this time, I can not promise any timeline for all of this. I am hoping for at least one post every week, but things could get hairy without warning.

Just like in the previous post, I am including another maze in this post, courtesy of my daughter. I have not had the time to prepare a full crossword puzzle for my blog yet. I have a few filled-in crossword puzzles, but I don’t have the clues prepared yet. Maybe next time. While I was away from my blog for the past 3 weeks, readers from exotic countries have not been so remiss: since my last update, I have had visitors from one new country on my blog. That visitor was from Kyrgyzstan. Talk about exotic! With this addition, I now have 167 flags in my flagcounter.

Now, it is time for me to wrap this up and get back to other work. I have work to do at work, work to do at home, and seemingly, work to do in between also. I know, all work and no play makes me dull, but hopefully, I will be able to finish all this up, and get back to more playing soon. Wish me luck, and ciao!

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