Friday the 13th Problem Solution

Friday the 13th Solution

Ok, I admit I'm a little late, and everyone's probably completely over the fact that there was Friday the 13th this month(Thats assuming they actually thought it was a semi-big deal in the first place!!). Well, since it occurred in the month of February which has 28 days this year, we're going to have another Friday the 13th in the month of March! 

Going back to the problem I posed, my high school teacher had a very simple solution to it. It made me feel pretty stupid trying to figure out some super fancy trick to find a solution to this answer. I ended up answering the question as (0,2) -- Meaning that the lowest number possible in a year is zero Friday the 13ths, and the maximum number was 2. Well, the right answer is actually (1,3) -- which caught me totally surprised!!! What it meant was that every year, we are guaranteed to have at least one Friday the 13th. I always used to think it was such a rare occurrence, but I guess it just seemed like it! 

Mr. Baker, my high school math teacher who supervised that contest sitting, starting out by assuming 'What if January 1st started on a Sunday????. This would mean that January 13th would actually fall on a Saturday. Since January has 31 days, February 13th would fall on a Tuesday. Again, on  a non-leap year, February has 28 days, and so March 13th would also fall on a Tuesday. Following that through, we get the following:

If January 1st was a Sunday then:

Saturday: January, October

Sunday: May

Monday: August

Tuesday:  February, March, November

Wednesday: June

Thursday: September, December

Friday: April, July

The above table tells us which days the 13th of that month falls on, assuming that January 1st was a Sunday. So, that year, April 13th and July 13th would fall on a Friday. However, January 1st could have occurred on any one of the 7 days, and we see that no matter which day it fell on, we will always have at least one Friday the 13th occurring each year, and at most, we'll have 3 Friday the 13ths occuring (that is when Feb/Mar/Nov 13 fall on a Friday) -- which will actually happen this year in fact!! We already had Feb 13th fall on a Friday. March 13 will follow soon, and so will Nov. 13th!!

So here you go -- I thought this answer was pretty simple -- The trick I guess is to approach every problem properly, and you can turn a hard problem into a fairly easy one!!! 

Broken Strings and Torn Shoes

Broken String:
So the other day -- and by that I mean yesterday of course -- I tore the string on my Apacs Nano 9600 Racket. It was about to tear for quite some time -- you can see one section of the main strings being cut through by the cross strings. So then I had to go back to my Yonex CAB30. After playing with it for a while, I've decided to return to it as my first choice racket now :). All of a sudden, my drop shots were much more improved, and I believe that is so due to the stiffness of the CAB30 racket. I guess I've improved enough over the last year to generate enough power even on that stiff racket! Once you tear a string, I've seen people cut up the rest of the strings with scissors!! The reasoning behind that is that once you tear a string, the tensions become unbalanced around the racket, and apparently, that *may* deform the racket -- but very minutely of course.

Torn Shoes as well:
Well, not only did I tear a string yesterday, but my 2 and half month old badminton shoes kinda started to come apart pretty bad -- so much that I can't use them anymore. They were from Asics (The Asics Gel Rocket IV shoe). The gum rubber sole was started to come off under my right heal, and it was starting to tear away. It really sucked!! I mean, I've only had the shoes for two and a half months. And I haven't played even played for a month around christmas time!! This wasn't really damage due to 'wear and tear' since I've never worn out a shoe that quickly. It must have been a product defect! So what I did today was I checked the Asics website to see what sort of warranty they have. Luckily, it mentioned that the shoes are warranted by the retail store that I bought it from. So I went back to the store, Sport Chalet, and guess what?? They took it back and exchanged the shoe to a brand new pair!!!! No questions asked!! Now thats a commitment to their customer. I like Sport Chalet a lot (www.sportchalet.com). And I guess after today, I'll make every effort to shop from their store whenever I can.

Friday the 13th

Since its Friday the 13th next Friday, I thought I'd post something dorky about it. When I was in high school, we used to have contest questions every now and then during the Math Club. One of those questions was actually about Friday the 13th. So here's the question:

In a given calendar year (leap years included), what is the maximum number and minimum number of Friday the 13th's that can occur???

This is an interesting problem, with a pretty sleek solution to it. Here's a clue to start you off: Actually, I'll tell you how I started it when I had to do it in the Math Club. I assumed that Friday the 13th's don't really occur all that often.. which seemed pretty reasonable at the time, and so said that 'zero' is the minimum number of Friday the 13ths that can occur in a year, and then proceeded from there. So now you're thinking, thats not a clue!! Its actually half the answer!! Well, the clue is: I was wrong :). Enjoy.

My Badminton Racquet History

The First One: Yonex Carbonex 8
The first racquet I ever used was a Yonex -- more specifically, a Yonex Carbonex 8. It was a hand-me-down, after my dad decided to get a new(better?) one in the form of a Yonex Carbonex 15. He later switched to the popular Carbonex 21. Me, on the other hand, spent a lot of time familiarizing myself with my Carbonex 8 -- something I'd thought would last forever. I don't remember too much of it right now, except that it was dark brown in colour, and I always made sure they were strung using black strings to add to the cool factor. It was a two-piece racquet -- meaning the shaft and head were attached through a T-Joint. It had the classic oval shape. Here's a picture from the Yonex website:

The Venerable Yonex Carbonex 8

I've used this racquet probably from Grades 8-12. I was on the Junior Varsity Badminton team during Grade 9 back in my old high school, and then again on the high school badminton team in Grades 11/12. This racquet lasted midway through Grade 12. I ended up cracking the frame sometime, but it was still intact -- until of course till the next time I tore the strings, and the racquet buckled under the stringing machine!!! The new Carbonex 8's are mostly 2U, so I'm guessing that's what mine was, but I have no clue as to what tension it was strung at. Just in case you don't know what the U's mean: the number preceding the U denotes the weight of the racquet. For example, 2U means that the racquet ranges from 90-94 grams. The two other common weights are 3U and 4U:
2U: 90-94 grams
3U: 85-89 grams
4U: 80-84 grams

My Second Racquet: ProKennex
My brother had this really REALLY lightweight Kennex Racquet, and I have no clue as to what its specs were. Apparently, Nafees still has the racquet, and it was loaned to our very Turjo Bhaiya, and has suffered the ol' DVD fate -- Its basically been borrowed indefinitely :)!

My Third Racquet: Yang Yang Dream 10

Yang Yang Dream 10 Racket

The moment I broke my racquet, I did what every other mature kid would do -- I went crying to my dad to buy me a new racquet from good ol' Abu Dhabi. It would arrive a month later, and soon enough, it arrived!! I was so excited, and I showed it off to everyone else in the badminton team. It was very light -- much much lighter than the free Carlton's the school's gym supplies had. I promised to treat it very carefully, so that it doesn't meet the same gruesome end as my first one, and I'm proud to say that I still have this racquet!! I finished off my Grade 12 year with this racquet, and then it went into hibernation for the next 6 years - thats partially the reason its still alive - other than the occasional badminton rush which occurred once every two or three years back then. Currently, its my third-choice backup racquet -- just in case my two other racquets miraculously become un-usable, which sounds totally plausible given my luck sometimes. I keep it strung at around 21 lbs of tension. I'll take a picture of it, and post it up sometime.

My Fourth Racquet: Yonex Carbonex 30 MS

Yonex Carbonex 30 MS Racket

Finally, after a horrendous injury-plagued 2007, I decided to get back into sports with style. After finding some places to play badminton in Arizona, I decided to invest in a new racquet. Actually, 'invest' isn't the right word! I believe 'splurge' does it more justice. In the back of my head, I've always trusted the Carbonex Series due to its popularity in Abu Dhabi, and decided to get the top-o-the-line one. And boy oh boy, am I sure glad I got it. Its an amazing racquet -- a little head heavy -- but still, it fit my play very nicely. Here are the specs:
Weight: 2U (Decided to get a heavier racquet, since its easier to transition from heavy to light than the other way round)
Flex: Stiff
Tension: 22lbs
String: BG-65 (Heck -- its cheap and durable :) )

My Fifth Racquet: Apacs Nano 9600 Tour

Apacs Nano 9600 Tour Racket

Compared the CAB30, the Yang Yang racquet wasn't really that great. So the first time I tore the strings on my CAB30, I had to use the Yang Yang one, and I wasn't too pleased. I decided to 'invest' (and yes, this time, I was able to control the splurging urge) in a good, durable backup racquet. After looking around a little on the web, I came across the Apacs line of racquets. There's a canadian dealership in that line, and its based in Toronto -- Markham to be exact. Their website is www.apacscanada.com. Basically, they make racquets which have the same specs as the expensive Yonex racquets (these are known as one of the many 'Yonex' clones), and sell them for much cheaper. Yonex racquets are darn expensive, mostly because they're....well...Yonex!!! With these other 'clones', not only do you get more or less the same racquet, but you get it a lot cheaper. BUT, to be fair to Apacs, they do make originals too which are specific just to Apacs, but I can't comment on them since I've never tried them. They have cool innovations though, such as a hard casing for the badminton racquet. I think that's absolutely brilliant :) in terms of trying to protecting a piece of equipment that can sometimes cost 200+ bucks! Anyways, so yeah, I got one of the Apacs racquets from Toronto, and after using it, I think its just as good as the Yonex ones, but at like a quarter of the price (50 bucks as opposed to 200 bucks!!). However, I think Apacs realized that they're doing well, and obviously jacked up the prices by 15-20% sometime last November, but they're still cheap though. I'm happy with this racquet, and in fact, it has now become my first choice racquet. More so because its a little lighter, and its not as stiff as the CAB30, and so helps my doubles play. I'd still probably use the CAB30 during tournaments though and singles play. The specs for this racquet are:
Weight: 3U
Flex: Medium
Tension: Main 26lbs, Cross 24lbs