Singapore Math

Tuesday, February 12, 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.”

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

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

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.

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

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.

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

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.

Wednesday, October 31, 2012

Halloween Math

A decade ago, celebrating Halloween in Singapore was considered a foreign import among locals, just like it was with Valentine's Day a quarter century ago. Today, local community centers and tourist attractions like the Singapore Science Centre and Night Safari (which is part of the Singapore Zoo), couldn't resist organizing their horrors nights to meet citizens' interest in the occult. As a result, many parents and teachers are faced with the dilemma as to whether to allow their children and students to participate in celebrations that had their roots in sorcery, witchcraft, and satanism.

For the rest of us who teach teenagers, who often like to dabble in, or experiment with, things occultic or satanic, how can we make use of some symbolism of Halloween, such as black cats, snakes, and broomsticks, to teach some creative problem solving in mathematics? How can we bewitch or bedevil them with "dark math," by entertaining them with some "wicked thoughts" about the most disliked subject in school?

Below are a baker's dozen of dark math problems we could pose to kids, who could get an intellectual kick out of solving them. Who says math and fear can't positively mix? Didn't someone say that God created the natural numbers, and all the rest is the work of man—and of the devil?

1. Dracula's Pets

Count Dracula collected an even number of insects (beetles and spiders) in his coffin. He counted 54 legs in all. How many spiders did he have?

13 is a "Lucky" number!
© ps3trophies.com

2. Friday the 13th and Halloween

Look at the following pattern:

13 × 13 = 169 and 31 × 31 = 961

Is this a mere palindromic oddity?

3. The Fewest Number of Coffins in a Day

On which day of the year do fewest people die?

i-Coffin
© cartoonbarry.com

4. Cemetery Math

On a tombstone is written the following:

R.I.P

Jasper Rice

Died: 31/10/85

Buried: 30/10/85

If there was no error or crime involved, explain this apparently impossible situation, which took place in October 1985.

5. The Secret Lives of Vampire Numbers

Numbers such as 1435 are called vampire numbers (or just vampires) because they are formed when two parent numbers (also called fangs), 35 and 41, are multiplied together (35 × 41 = 1435). Another vampire number is 2197, because it contains digits of its fangs, 27 and 81 (27 × 81 = 2187).

(a) Are there any two-digit vampire numbers?

(b) How many 4-digit vampires are there?

6. A Deadly Will

A dead man's will states that seven bats were to be divided among his three ungrateful sons. The eldest was to receive one half of the bats, the middle one, one-fourth, and the youngest, one-eighth.

The three wicked sons had nightmares as they couldn't inherit their shares without cutting bats into parts.

They sought the help of a wise priest who suggested that he would lend them one bat so that a “fair” allocation could be possible. The eldest son would then receive 1/2 × 8 = 4 bats, the middle one, 1/4 × 8 = 2 bats, and the youngest one, 1/8 × 8 = 1 bat. Thus, the sons would receive 4 + 2 + 1 = 7 bats, returning the borrowed bat to the holy man. Is the priest's solution “fair”?

7. Halloween Falls on a Frightday!

In a complete period of 400 years (after this, the calendar repeats another similar cycle), which day of the week is Halloween mostly likely to fall?

8. Legion's Number

In the Gospel of Mark, Jesus encounters a multitude of demons possessing a man. When the Son of Man asked them, "What is your name?" the man replies, "My name is Legion, for we are many."

The computer scientist, Clifford A. Pickover, defined the number 666⁶⁶⁶ as Legion's number of the first kind, and the number 666!⁶⁶⁶^! as Legion's number of the second kind.

(a) What are the last 31 digits of 666!?
(b) What are the last ten digits of 666!⁶⁶⁶^!?
(c) Using a computer, what are the last ten digits of 666⁶⁶⁶?

By definition, 666! = 1 × 2 × 3 ×⋯× 665 × 666

9. The Math of 9/11

Using the pattern and period of the calendar, and the day of the week September 11 falls this year, what day of the week was 9/11—the "Holy" 2001 War by the "fidels" on the Twin Towers?

10. Is Phi Divine or Demonic?

An equation uniting the Number of the Beast 666 and the golden ratio ø is given by

ø = −{sin 666º + cos[(6)(6)(6)º]}

Verify phi's apparent liaison with the satanic number.

11. A Grave Calculation

How long will it take before the whole

world is covered in gravestones?

Hint: What is the total land area on Earth?

How much area does each person's grave take up?

12. Triple 4 and Triple 6

The Chinese avoid the "death number" 444; the Westerners avoid the "satanic number" 666. The West like the number 7 and multiples of 7, while the East like even numbers but avoid odd numbers. In general, Asians' "lucky" numbers are Westerners' "unlucky" numbers.

Why do both the East and the West still have faith in numerology and astrology, in spite of literacy, numeracy, and technology?

13. Santa versus Satan

It is said that Satan is a wolf in sheep's clothing: f(Santa) = Satan.

Prove that Oct. 31 = Dec. 25.

References

Pickover, C. A. (2002). The mathematics of Oz. Cambridge University Press.

Pickover, C. A. (1997). The loom of God: Mathematical tapestries at the edge of time. New York: London Plenum Trade.

Santos, A. (2009). How many licks? Philadelphia: Running Press.

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

Selected Answers

1. 3 spiders and 5 beetles.
Spiders have 8 legs and beetles 6.
We need to solve 8s + 6b = 54 with s, b positive and s + b even.
Hence there are 3 spiders and 5 beetles.

3. On the same day that the fewest people are born—29 February.

4. The man dies on a Monday and his body was then flown across the International Date Line to a place where it was still Sunday for immediate burial.

5. (a) No 2-digit vampires exist.
(b) 7 four-digit vampires.

8. (a) They are all zeros.

The last digits of 666! are 0 because 5¹⁰ and 2¹⁰ both divide 666! The number 666! has well over 100 zeros.

(b) The last 10 digits of 666!⁶⁶⁶^! are 0.
(c) The last 10 digits of 666⁶⁶⁶ are 0,880,598,016.

Challenge: What are the first 10 digits of Legion's number of the second kind?

9. Tuesday.

11. More than a million years.
Hint: How many people die every year round the globe?
Time taken = (Total area of the Earth) ÷ [(Number of dead people per year) × (Area per dead person)]

13. If "Oct." is the short form of "octal" and "Dec." for "decimal," then 31 (in base-8 notation) is equal to 25 (in base-10 notation): 31₈ = 25₁₀

© Yan Kow Cheong, October 31, 2012

Singapore Math

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Tuesday, February 12, 2013

How to Choose Your Marriageable Date

Wednesday, October 31, 2012

Halloween Math

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