Expensive-Cheat Singapore Math Books

In recent years, a certain genre of mathematics titles had flooded the Singapore assessment (supplementary) market to meet the needs and wants of kiasu parents, who want to ensure that their children have a competitive edge over their peers.

One conspicuous series of such assessment titles in our local bookstores is published by Amazing Books. The Primary 1 - 3 titles (selling from $8.00 to $9.90) are written by a certain Newton Wong, while Primary 4 - 6 titles (selling from $11.00 to $12.50) are written by an Ernest Wong—it’s hard to confirm whether the writers are ghosts or not. These supplementary titles generally cost as much as a Ministry of Education (MOE)-approved primary textbook—however, they're value-for-money titles, if you're agnostic as to whether copyrights have been safeguarded or not.

Wallet-friendly titles that may meet the
mathematical needs and wants of kiasu parents

Indeed, there is much to be gained from writing these assessment titles, as compared to, say, authoring an MOE-approved textbook which goes through the tedious reviewing exercise by the Ministry of Education, the approving body of Singapore textbooks. 

Critics (mainly authors of traditional assessment books) arguably claim that these “cheat-expensive books” or "expensive-cheat books," as they’re called in local educational publishing, are nothing but a rehash of faintly modified past exam questions from the top or popular schools in Singapore.

High Price, Low Content

Another category of expensive-cheat titles involves those whose contents don't justify their selling prices—titles that over-promise and under-deliver. Come with quality paper, some look pretty good in form but shy of substance. 

Note however that the use of the word “cheat” doesn’t in any way suggest that the writers had plagiarized the contents, although it’s not uncommon for teachers and tutors to suspect that in some cases plagiarism could have inadvertently taken place. 

At best, these expensive-cheat titles provide information for readers new to the subject matter at a high price; at worst, these titles are copycats of pirated test papers or canned contents that have been put in a form that are readers-friendly.


Piracy Goes Online

Here is a typical ad spammed probably to tens of thousands of homes every few months:

Top Schools' Test Papers (Yr 20XX) on CD 

Hi Parents Give your child a head-start at school by Practice Doing Top Schools' Test Papers This will help your kids to Score !!! *Primary 1  -  Primary 6 ( SA1 & SA2 papers ) *Data is in scan-in PDF format *English, Maths, and Science *Answers also provided *Only $5 per subject !( Min order 3 subjects @$15 only ) **3-Year Series : P5 SA2 / P6 Prelim ( Yr 20XX - 20XX )     3 yrs x 3 subjects @$15 only ( total about 50 sets testpapers ) **Also available : Sec.1 - 4 SA2/Prelim  Maths :( Yr 20XX ) @ $10/subject Call Now !! XXXX XXXX * NB *  To unlist pls click < HERE > thank you. A kiosk outside a shopping mall, selling past exam papers from allegedly top schools. Plagiarism Begets More Plagiarism Grade 4 questions that mimic those set by teachers in "top schools"—these "model answers" are quasi-edited "solutions." It’s an irony that while many fly-by-night writers had modified questions from the top schools’ exam papers with cosmetic changes; yet, often times, some teachers from these same schools are equally guilty in lifting up large chunks of content from assessment titles, by photocopying and distributing entire chapters to their students and fellow colleagues. Plagiarism begets new levels of intellectual theft. Unscrupulous vendors know too well that the MOE would find it hard to crack down on these perpetrators of piracy. After all, few parents could detect the authenticity of these questions—whether or not they’re really set by teachers from allegedly top schools. Most questions look challenging to the clueless parents, who would buy anything which would help their children do well in the subject.  Two Wrongs Don't Make a Right If half-baked or poorly edited solutions isn't much of an issue, these tips-and-tricks titles may appeal to some students who can't afford private tuition. Lest their children lose out vis-à-vis their peers, most kiasu parents wouldn’t give a second thought to buying these pirated sets of exam papers. The rationalization is that since the MOE refuses to sell them, they’ve little or no choice but to procure them from illegal vendors. The means to laying their hands on these sought-after papers justifies the end—that these non-routine questions would prepare the child confidently for his or her school test or exam. With home delivery service of these syndicated or pirated papers at no extra costs, parents can now feel less guilty, as they could avoid being seen buying these illegal papers in public. And for IT-savvy consumers, they’d now order these papers online, at a cheaper price, if they want an electronic version of them. A Copycat of Top Schools’ Exam Papers A grades 7-8 supplementary title that may be suitable for drill-and-kill specialists—it's priced at S$24.95 in retails outlets. Unknown to many of these authors, the international mathematical community of mathematics educators often poke fun at the poor quality of our local assessment or supplementary mathematics titles. Many writers have probably not read what math educators out of Singapore are saying about their dear titles, especially when they're marketed overseas.  Leaving poor design and linguistic blunders aside, these expensive-cheat local titles are often an embarrassment to the image of Singapore mathematics publishing, as the nation strives to become an educational and publishing hub in Asia. In recent years, it's an open secret that questions from so-called top schools are actually the works of syndicates, which recruit Indian and mainland Chinese nationals, and cash-strapped undergraduates, to write math questions that mimic those posed by teachers from top schools. The Works of Syndicates No one is surprised that these expensive-cheat titles are a few folds pricier than the traditional assessment titles. These often ill-written supplementary titles, which make unverifiable claims to parents and teachers, will continue to thrive if the authorities don't get down to verifying the authenticity of the questions, and as long as the consumers continue to purchase them, pretending that they’re unaware that they're MOE-copyrighted materials. While the MOE authorities should take a share of the blame pie for not making schools' test papers available for sale, very often, it’s those teachers with an entrepreneurial spirit who are probably the source of these copyrights infringements. Who can have access to these exam papers if students and outsiders are not allowed to take them out of the school compound? The non-routine questions are suitable for grades 5-6 students, but the solution methods sometimes lack rigor, and a number of them are poorly presented and edited.  Although there is no formal investigation on these assessment titles claiming to contain contents that match the questions commonly set by Singapore's top schools, it doesn’t take a DNA scientist to figure out that most of these assessment papers were probably lifted up from test questions, which have undergone some cosmetic rewriting to avoid being caught (or sued) for blatant infringement of copyrights. The sale of most past exam papers from government schools is officially illegal; yet, every local knows how and where to buy them. The public knows that schools and the MOE don’t have the resources to sue the guilty parties. It wouldn't be surprising that some education officers are themselves part of the piracy syndicate. How would syndicates have had access to those past exam papers in the first place had they not been leaked out by teachers or school personnel themselves? Indecent Photocopying Over the years, I’ve personally heard from a number of assessment authors who had complained to the MOE that some top schools’ HODs had blatantly plagiarized their contents to be used in workshops and seminars, or that some teachers had made an indecent number of copies for an army of students. Of course, the standard answer from the MOE was that they’d look into the matter, and before you know it, the whole saga has faded away.  As long as we pay lip service to the intellectual rights of math writers and authors, and the infringement of  copyrights is condoned among teachers and students, the future of math publishing in Singapore doesn't look too bright. In fact, the quality of future Singapore math titles is likely to suffer further, as more and more non-math graduates are recruited as math editors in local publishing houses.  © Yan Kow Cheong, May 29,  2013.

The Chickens-and-Cows Problem

At the end of an earlier post entitled "The Chickens-and-Rabbits Problem," I tickled readers whether the following question could be solved using the Singapore model method, or the Sakamoto method.

Mr. Yan has almost twice as many chickens as cows. 

The total number of legs and heads is 184. How many cows are there?

On his "Johnny and Mary Do Maths" blog, Chris Patterson followed up with an algebraic solution to the word problem in a post entitled Visualisation versus Algebra?. He asked me whether I have a visual proof to the question, particularly one using the Sakamoto method.

I'm not sure whether I've succeeded in answering Chris's question, but here are three quick-and-dirty non-algebraic attempts to the chickens-and-cows problem.


Method 1 (Singapore model method)

From the model,

11 units = 184 + 3 ▌= 16 × 11 + (8 + 3 ▌)

If ▌= 1, then 11 units = 16 × 11 + 11

          1 unit = 17

2 units – 1 = 2 × 17 – 1 = 33

A quick check shows that for other integral values of ▌other than 1, 11 units cannot be an integer.

Hence, Mr. Yan has 33 chickens and 17 cows.


As a student of the Singapore model method, still trying to learn how to make wise use of this visualization strategy, especially when it lends itself well to a particular word problem, I would like to hear from members of the Singapore mathematical brethren about their alternative models in solving this chickens-and-cows problem, assuming that we're discussing this question with a group of grade 5 or 6 students—with no knowledge of Diophantine equations or advanced algebraic techniques.


Method 2 (Sakamoto method)

1. Grasp the relation

Let ① represent the number of cows, and △ be a variable quantity that is much less than ①.

                                           Chickens            Cows

                                              ② – △                ①

Number of legs                 (② – △) × 2         ① × 4

                                            = ④ – 2△            = ④

                                   _________________________

                                                           184

2. Diagram

3. Number sentences

② – △ + ④ – 2△ + ① + ④ = 184
⑪ – 3△ = 184
⑪ = 184 + 3△ = 16 × 11 + (8 + 3△)

If △ = 1, then ⑪ = 16 × 11 + 11 = 17 × 11
                       ① = 17
② – △ = 2 × 17 – 1 = 33

So, there are 17 cows and 33 chickens.


Unless there's a more elegant Sakamoto solution, I find that it doesn't differ much conceptually from its algebraic cousin.


Method 3 (Using the "Make a supposition" strategy)

Suppose there were exactly twice as many chickens as cows.

Then each group of 2 chickens and 1 cow would have a total of [(2 + 2 × 2) + (1 + 1 × 4)] = 11 legs and heads.

Now, 184 = 11 × 16 + 8

16 groups of 2 chickens and 1 cow would have a total of 16 × 11 = 176 legs and heads.

How many chickens and cows have 8 legs and heads altogether?

Clearly, 1 chicken and 1 cow have 8 legs and heads altogether.

So, Mr. Yan has (16 × 1 + 1) = 17 cows and (16 × 2 + 1) = 33 chickens.


Conclusion

With Chris's algebraic solution, we're sharing four methods of solution to the chickens-and-cows problem. Which method do you prefer? Which one would you use with your students? Share yours with the rest of us.


© Yan Kow Cheong, April 24, 2013.

A Vintage Age Problem

While surveying some age problems in Joseph Degrazia's Maths Is Fun, I came across the following 1949 word problem.

Bill is twice as old as Sam was when Bill was as old as Sam is. 

When Sam is as old as Bill is now, both of them together will be 90. 

How old are they?

Since no solution was given in the book, I assume that the author then would most likely expect the problem solver to use an algebraic approach to solving it.


Language and Logic

I needed to read the question a few times, before I felt confident that I was in control of the problem situation. That made me believe that one major obstacle for students attempting to solve this vintage problem would be to really understand what the question is all about—how the ages of Bill and Sam are related at different times.

However, regardless of the method of solution used, this word problem might also prove to be quite a challenge to those who are learning English as a second or third language.


The Model Method as an Ideal Choice

Among competing non-algebraic approaches, especially if this question is assigned to grade 5 or 6 students, my methodological bias in favor of the Singapore model method convinces me that a visual approach would offer an elegant, if not better, solution to the problem, as compared to an algebraic method of solution; in fact, the word problem does lend itself quite well to the model, or bar, method. Try solving the question, using the model method, on your own first, before peeping at a suggested model-drawing solution below—you may even come up with a better model than mine.

Here's a quick-and-dirty Singapore model solution to the above vintage age problem.

Observe that the age difference between Bill and Sam is always one unit.

From the model,

9 units = 90

1 unit = 90 ÷ 9 = 10

3 units = 3 × 10 = 30 ➝ Sam

4 units = 4 × 10 = 40 ➝ Bill

Bill is 40 years old.

Sam is 30 years old.

When Bill was 30, Sam was 20.

When Sam is 40, Bill will be 50 and both will be 90.

An inexpensive supplementary title to learn
the Singapore model method confidently. 
Visit singaporemath.com

Conclusion

Even for students who like math, the trouble with this age problem isn't just about exhibiting clear thinking and reasoning, but also about language proficiency. Language and logic, particularly in this case, each play an important part in the thinking process in producing the correct product. Moreover, a model-drawing solution to this vintage problem also shows that this question, which would normally be solved algebraically at a higher level, could be posed to students at a lower grade.


Reference
Degrazia, J. (1949). Maths is fun. London: George Allen and Unwin Ltd.

© Yan Kow Cheong, April 12, 2013

The Mathematics of the Cross

Amazing love! How can it be

that thou, my God, shouldst die for me?

from Thomas Campbell The Bouquet 1825

Flag of Red Cross

The cross isn't just a sacred icon or symbol for religious math educators, but it's also a geometrical shape that has borne much fruit in producing many logic and mathematics puzzles. Few recreational mathematicians, professional and amateur, wouldn't want to be challenged by these fertile dissection puzzles.

Flag of Switzerland

Let's resurrect some of these ancient cross puzzles, which have given so much intellectual satisfaction to those who have decided to take up their cross along their mathematical itinerary. Below are ten of these Christmaths puzzles, which would appeal to above-average elementary and middle-school math students and their teachers.


1. Squares in a Cross

A solid Greek cross can be formed by putting together five cubes, or from a number of squares. How many squares are there?

2. Tessellating and Dissecting Crosses

(a) Show how Greek crosses can form a tessellation.

(b) How can an infinite number of dissections from a cross tessellation produce a square?





3. A matchstick Puzzle

The cross on the left is made up of 19 matches. Move 7 of them to make a pattern consisting of four squares.




4. The Area of a Cross

A cross is made up of five congruent squares. If XY = 10 cm, what is the area of the cross?

5. Cross into Rectangle

Using only two straight cuts, divide the cross on the right into three pieces and reassemble them to form a rectangle twice as long as it is wide.




6. Five-piece Square into Cross

Cut a square into five pieces and rearrange them to form a Greek cross, as shown below.

7. Four-piece Square into Cross

Cut a square into four pieces and rearrange them to form a Greek cross, as shown below.

8. Cross into Hollow Square

The Greek cross on the left has a square-shaped hole in the center. 
(a) Rearrange the pieces to make a square that has a hollow cross inside.
(b) Rearrange the pieces so that the resulting figure is a square that is rather smaller than the previous "hollow" one. 



9. The Cross and the Crescent 

Reassemble the seven pieces of the crescent to make the Greek cross.

10. The Rolling Disc

In the figure below, each side of the cross is 10 cm long. A small circular disc of radius 1 cm is placed at one corner. If the disc rolls along the sides of the figure and returns to the starting position, find the distance traveled by the center of the disc. 

Selected answers/solutions

1. 22 squares.
4. 100 cm².
5.













7.








8.








10. (104 + 2π) cm

Reference
Yan, K. C. (2011). CHRISTmaths: A creative problem solving math book. Singapore: MathPlus Publishing.

© Yan Kow Cheong, March 31, 2013.

Code: WR3ZTVKVUW9Z

31 Reasons to Smile

1. A Facebook invitation to connect with a long-lost friend thousands of miles away—across the other side of the continent.


2. Finding geometric shapes in the clouds.


3. The smell of a math book fresh from the printer.


4. Seeing someone helping a blind 70-year-old crossing the road.


5. Your child sneaking in her phone even when she's answering to nature's call.


6. Your daughter undecided whether she'd go out with that boy from her class.

7. Double rainbows.

Double Rainbow
© www.vibrantnation.com

8. Hearing that a friend or colleague has successfully gone through her chemotherapy sessions, and she's recovering fast.

9. The public library opens on Boxing Day.

10. Finding the clue to solving a mathematical problem.


11. Going to a public forum and finding that the free food tastes better than those served at five-star hotels.


12. Middle-aged women with heavy make-ups and dyed hair, and they look pretty ugly!


13. Men and women who wear winter clothes in humid, hot Singapore.


14. Your hamster or guinea pig which greets you when you come back home.


15. When you find that you're the only one using the toilet, or the only passenger in a public bus.

16. Ordering a dessert you hadn't had for ages at a food carnival.

17. A free copy of a newly published book from an author-friend himself, which you plan to buy at your next visit to the bookstore.

Junk Mail
© www.toonpool.com

18. Grammatically correct spam e-mails, where the language proficiency is better than those sent by your editors.

19. Being able to access your e-mail at a location you thought would not receive a Wi-Fi signal.

20. Preachers who blushed on expounding on topics such as sex, lying, and secret sins.

21. Hearing someone fart loudly in a train or in a public library.

22. Seeing semi-naked men whose breasts are larger than those of most women.

© cakeordeathcartoon.wordpress.com

23. An old folk nervously solving a sudoku.

24. Receiving those politically correct rejection letters, saying that your skills don't match the requirements of the post applied.

25. The seat next to you staying empty on a plane.


26. Shopkeepers who use the abacus to find the total amount you need to pay.


27. Remember composing your first SMS or e-mail.


28. Finding an out-of-print math book at a second-hand bookstore.


29. Spotting a slide rule or logarithm table at a flea market—vintage math.

A typical 20th century slide rule  
© cai.cam.ac.uk

30. Your average grade seven math student giving private tuition to a grade two student.


31. Seeing your child solve an elementary math problem that you couldn't solve when you're at her age.

© Yan Kow Cheong, March 18, 2013

The Dogs-and-Ducks Problem

Recently, while reviewing some grade 5 olympiad questions for a local company, which specializes in conducting olympiad math programs in elementary schools, I came across the following nonroutine dogs-and-ducks question.



The number of ducks is 10 fewer than the number of dogs. 
The dogs have three times as many legs as the ducks. 
How many ducks and how many dogs are there?



When I realized that my mental calculated answer differs from the one given by the problem poser, I thought maybe my incorrect solution might serve as a "logic exercise" to tickle others' mathematical bones to point out the flawed reasoning. My faulty argument followed something along these lines:

Since there are 10 fewer ducks, and each duck has 4 legs, there are 10 × 4 = 40 fewer duck legs.



From the model drawing,



2 units = 40


1 unit = 20



Number of duck legs = 1 unit = 20


Number of ducks = 20 ÷ 2 = 10



Number of dog legs = 3 units = 3 × 20 = 60


Number of dogs = 60 ÷ 4 = 15



A quick check shows that the answers don't satisfy the given conditions in the question. Although the dogs have three times as many legs as the ducks, however, the number of ducks is only 5 fewer than the number of dogs, which is expected to be 10.




When the why is harder than the how



The lesson here is to identify the illogical step, although seasoned problem solvers would probably not commit this kind of error or blunder. 

In general, it's one thing not to make an error, and get the correct answer; it's another thing to be able to explain someone else's error.

At a deeper level, it's sometimes conceptually harder to explain someone's flawed reasoning to an incorrect answer than just know how to solve a problem. Think of mathematical fallacies and paradoxes, where in a number of cases the illegal step is anything but obvious.




A fabricated faux solution

Alternatively, if we argued that a dog has 2 more legs than a duck, we'd then have a model that looks like this:

In this case, students would easily realize that the answers are also incorrect, when they find out that the number of dogs isn't an integer.


Two quick-and-dirty solutions

Why don't you try solving the dogs-and-ducks question on your own first, before comparing your solution with the ones I've worked out? If yours is an alternative (or elegant) solution, the mathematical brethren couldn't wait to reading it!

Method 1

Since a dog has twice as many legs as a duck, and there are 3 times as many dog legs as duck legs, there are 3/2 times as many dogs as ducks.

A model depicting the above relationship may be drawn as follows:

From the model drawing,

1 unit = 10

Number of ducks = 2 units = 2 × 10 = 20

Number of dogs = 3 units = 3 × 10 = 30

Check: Ducks: 20 × 2 = 40 legs

Dogs: 30 × 4 = 120 legs = 3 × 40 legs

Method 2

Given: Number of dogs = Number of ducks + 10

Number of duck legs = 2 × Number of ducks

Number of dog legs = 4 × Number of dogs

Given: Number of dog legs = 3 × Number of duck legs

A quick-and-dirty model representing the above information may be drawn as follows:

From the model drawing,

3 × 2 units = 6 units = 4 units + 10 + 10 + 10 + 10 

2 units = 10 + 10 + 10 + 10

1 unit = 10 + 10 = 20

1 unit + 10 = 30

Therefore, there are 20 ducks and 30 dogs.

Method 3 (Sakamoto method)

Those of you who are versed with the three-step Sakamoto method in solving word problems, may proceed as follows:

1. Grasp the relation

Let ④ represent the number of duck legs.

Duck legs           Dog legs

④                     ⑫

__________________________

Number of ducks     Number of dogs

④ ÷ 2 = ②                 ⑫ ÷ 4 = ③

                                             – 10

__________________________

1              :              1

                             + 10

2. Diagram

3. Number sentences

③ – ② = ① = 10

② = 2 × 10 = 20 (ducks)

③ = 3 × 10 = 30 (dogs)

The number of ducks is 20, and the number of dogs is 30.

Two bonus problems

If you like being challenged by similar dogs-and-ducks or chickens-and-rabbits problems, may I direct you to solving two more questions at Yan's One Minute Math Blog?

Happy Mathematical Problem Solving!


© Yan Kow Cheong, March 3, 2013

How to Choose Your Marriageable Date

If you were of marriageable age and weren't superstitious, how would you go about choosing your wedding date, one that would help you to remember your wedding anniversary for a long time? One rational, yet free, approach is to choose a “marriageable date.”

© www.pgcmis.info

A marriageable date may be defined as one that is based on some simple numerical pattern, which a couple can easily remember long after the wedding day is over.

Socially speaking, marriageable dates ought to be religion-free and race-free—they should be derived from some easily recognizable patterns.

Economically speaking, it doesn’t cost more than a few drops of ink to write the memorable date, free from any numerological calculation or influence of a fortune-teller or New Age charlatan.

Sociologically speaking, tying the knot on a marriageable date helps you to divorce yourself from any irrationality and superstition that certain dates in a given year are more auspicious than others.

Palindromic Dates

© www.thegloss.com

A palindrome is a word that spells the same when read forward or backward. For instance, MADAM and EVE. And some palindromic sentences or phrases that sound mathematical are

           I prefer pi.          Never odd or even

In mathematical parlance, a palindromic number is one that reads the same when its digits are reversed. Examples of palindromes are 101, 313, 10301, 23432, and 3535353.

Now, let's look at some palindromic dates, the British way:

11th November 2011: 11/11/11         11th February 2011: 11/02/2011     

21st November 2012: 21/11/12          21st February 2012: 21/02/2012

31st March 2013: 31/3/13                 31st August 2013: 31/8/13

@ NewYorker: A palindrome cartoon by Paul Karasik

Prior to 2013, we had "hot dates," such as the following:

20th November 2012: 20/11/2012 or 20112012

20th December 2011: 20/12/2011 or 20122011

20th December 2012: 20/12/2012 or 20122012

What about 20th December 2013? 20/12/2013 or 20122013

Other patternful or pseudo-patternful dates in 2013 are:

            1/12/13            2/11/13            12/1/13            9/11/13

            13/2/13            13/11/13          11/12/13          11/2/13

The Beasted Date

© www.spreadshirt.net

On 6th June 2006, the date was “060606”—the beasted date that would have made some hardcore believers sick, sick, sick! But in Singapore, it was considered an “auspicious" date which led 310 couples to tie the knot at the Registry of Marriages (ROM). And in Penang, Malaysia, 89 couples also took advantage of that allegedly “lucky” date.

On 3rd March 2003, the date “030303” drew 163 weddings. Based on the DDMMYY pattern, there was also a record of couples tying the knot on 12 December 2012.

© www.redbubble.com

The Friday the Thirteenths

Another group of quasi-marriageable dates that superstitious couples usually avoid are those that fall on a Friday the 13th. Two such “unlucky” dates in 2013 that rational folks could leverage on to book their D-Days are:

13th September: 13/9/13

13th December: 13/12/13

The Ghost Month—a Most Marriageable Month

Inauspicious or ill-omened dates superstitious Chinese couples shy away occur during the Seventh Lunar Month, or Ghost Month. This is when rational and budget-conscious couples ought to hold their weddings—when most hotels are charging patrons a promotional rate. Besides, since many irrational or fearful couples avoid tying the knot during the seventh month, the saving for holding a grand wedding at a five-star hotel, at a reasonable price, on any of those "unlucky" days, can be quite significant.

Dates with Consecutive Numerals

One set of marriageable dates involves having the day, month, and year in consecutive order:

8th July: 08/07/06                 9th August: 09/08/07

13th December: 13/12/11      11th December: 11/12/13                

Odd- and Even-numbered Dates

Another set of hot wedding dates have the day, month, and year, in increasing or decreasing multiples of a whole number.

8th October: 8/10/12             9th November: 9/11/13   

7th October: 7/10/13              4th August: 4/8/12                  

3rd August: 3/8/13               14th December: 14/12/10

                                               

How many such marriageable dates are there in the Lunar Year of the Snake?

Sierpinski Valentine
© xkcd.com

D-Day on Valentine's Day

A record 1080 couples registered their marriage on Valentine's Day in 1995, as the Chinese considered it a Double Happiness Day—it coincided with the Chinese version of the Valentine's Day, also known as yuan xiao jie, which is on the 15th day of the first month of the Chinese New Year. What's your prediction on February 14, 2013?

Symbolically, tying the knot on Valentine's Day may prove memorable, but unaffordable to many couples as they look for a wallet-friendly hotel to hold their wedding and their subsequent wedding anniversaries.

Date and Time Included

© wjmc.blogspot.com

If we marry the time with the date, more interesting patterns emerge. For example, on 4th May 2006 at 8 minutes and 9 seconds, after 7am, the date and time spelled out as

               04. 05. 06. 07. 08. 09

Or, on 5th June 2007 at 9 minutes 10 seconds past eight, we had:

                                               

               05. 06. 07. 08. 09. 10

Can you think of some memorable dates in 2013 and beyond, following a similar pattern?

British (UK) versus American (US) Dates

All the above patternful dates and times are based on the British way of writing dates and times. If we write dates and times the American way, a new set of marriageable dates are generated.   

© www.joy-of-cartoon-pictures.com 

In British English, dates are generally written with no comma between the month and year: 7 May 2013. American English prefers the style May 7 2013 or May 7, 2013.

In numerical notation, there is a difference: 7/5/13 means 7 May 2013 in Britain and 5 July 2013 in America.

So, decide in advance whether you want to wed in a country where they follow the British or American system of writing numerals. A rational option may save you a few hundred or thousand bucks!

Conclusion

© taiwanbrown.com

The beauty and utility of marriageable dates is that they don't have to tie up with astrology or geomancy to be sanctioned—they're free from any pseudoscientific influences, which would save you, at the least, a few hundred or thousand dollars and months of headache. Marriageable dates are based purely on meaningful patterns; besides, they provide no excuse for any party in future to forget their wedding anniversary. Indeed, nothing is left to chance and randomness, or fear and superstition.

Patternful dates are more interesting and memorable than geomancized or numerological dates. In addition, a by-product of marriageable dates can prove mathematically educational, as compared to feng shui-formulated dates, which are credulously auspicious and costly. One is based on logic and reason; the other is based on irrationality and fear. So, let's marry reason and patterns to choose our wedding date, while divorcing ourselves from any superstition and irrational fear.

Questions

1. How many palindromic “marriageable dates” are there in 2013, if they are written in both British and American English?

2. A set of hot wedding dates have the month, day, and year, in ascending or descending order. For example, 9/11/13 and 12/10/8. How many such odd- and even-numbered dates are there in 2013, if dates are written the American way?

3. On October 11, 2012, at 8 minutes and 9 seconds after 7 o’clock, some Americans expressed the time as follows: 07. 08. 09. 10. 11. 12. How many similar dates can be expressed in this century? How would the answer change if the dates were written the British way?

4. Who would be "luckier," by having more "marriageable dates" in a typical year? Those who write their dates the American or British way? Explain.

References

Deng, Fern (2006). Devilish or not, 666 is hot wedding date. The Straits Times, June 7, 2006, p. H4.

Koh, Melody (2006). 06.06.06 was a lucky date for them. Today, June 7, 2006, p. 6.

A devil of a date. The Straits Times, June 5, 2006, p. 12.

'030303' draws 163 weddings. Streats. March 3, 2003, p. 2.

© Yan Kow Cheong, February 12, 2013.