In the aftermath of the death of Singapore’s founding father, Mr. Lee Kuan Yew (1923–2015), a number of *numerological tidbits* (or *numerical curiosities*, to put it mildly) floated on social media, which got a number of apparently self-professed innumerates pretty excited. Here are three such postings that I saw in my Facebook feed and on *WhatsApp*.

**RIP: Lee Kuan Yew (1923–2015)**

The *WhatsApp* message gives the impression that it was the works of some “pseudo-mathematician,” but it could very well have been the digital footprints of a “mathematical crank” or an amateur-numerologist, who wanted to tickle mathophobics with such numerical coincidences.

Did Singapore’s numerologists (or pseudo-mathematicians) fail to point out some of the following numerological absurdities?

The *digital root* of Mr. Lee’s birth year is 1 + 9 + 2 + 3 = 15, which stands for the last two digits of the year he experienced his last heartbeat.

The pollution index for that week was in an unhealthy range, and the average PSI for the six-day mourning period was about 91.

Or, were there exactly 91 priests on vigil at an undisclosed Roman Catholic Church, who were interceding for Mr. Lee to ensure that his heavenly destination is 100% secured, although his manifold deeds to the nation inarguably exceeds the number of his political *faux pas*, especially *vis-à-vis* his political enemies or opponents?

Or, did 91 senior monks and nuns (or did I mistake them for disciples of Shintoism?) resort to “synchronized chanting” to ensure that the highest level of enlightenment be bestowed on the late Mr. Lee, who might be reincarnated as a future Buddha for his numerous selfish deeds towards his oft-ungrateful and unappreciative fellow citizens?

And did any police personnel verify whether there were 91,000 odd mourners in black attire on that *Black Sunday*, not to say, 91 VIPs or Heads of States who attended the eulogy, depending on one’s definition of a VIP?

**The Numerology of the Old Guard**

One Facebook numerological factoid that circulated in the first post-LKY week was the following:

At face value, these nonagenarians had their blessed lives prolonged up to “four scores and ten and one” years. Sounds like their good earthly or political deeds were good karma for their longetivity? Are they the recipients of the following success equation?

**Sacrifice + Service + Incorruptibility + Risk = Political Success + Longevity**

**Sacrifice + Service + Incorruptibility + Risk = Political Success + Longevity**

Observe that simply taking the difference between the birth year and the death year of Mr. S Rajaratnam suggests that he died at the age of 91; however, if we look closely at the month dates (Feb. 25, 1915 – Feb. 22, 2006), he was still 90 years old, when he passed away. The same argument goes for Dr. Toh Chin Chye (Dec. 10, 1921 – Feb. 3, 2012), who wasn’t yet 91, when he died. So, always take the pseudoscience of numerology with a grain of salt. As with *fengshui* charlatans, a degree of skepticism towards numerologists of all sizes and shapes isn’t an option—wear your critical-thinking cap when meeting, or reading about, these paranormal folks!

*Fortune* via *Misfortune—*From 4D to 5C

*Fortune*via

*Misfortune—*From 4D to 5C

To rational non-punters or non-gamblers, betting on someone’s death date, whether he or she was poor or rich on this side of eternity, seems like an extreme case of bad taste, or simply showing zero respect for the deceased and their family members. However, in superstitious circles, that practice isn’t uncommon among mathematically challenged or superstitious punters, who think that bad luck paranormally translates into good omen, if they bet on the digits derived from the death date or age of a recently deceased person.

In fact, during the nation’s six-day mourning period for its founder, besides the long queues of those who wanted to pay their last respects to Mr. Lee at the Parliament House, another common sight islandwide were meters-long lines of 4D or TOTO punters, who wanted to cash in on the “lucky digits” to retire prematurely, hoping to lay hold of the traditional 5Cs (*cash*, *car*, *condo*, *credit card*, *country club*), coveted by hundreds of thousands of materialistic Singaporeans.

*Number Theory* over *Numerology*

*Number Theory*over

*Numerology*

Instead of promoting a numerological or pseudoscientific gospel based on Mr. Kuan Yew’s death date or age, which only helps to propagate superstition and pseudoscience, perhaps a “mathematically healthy” exercise would be to leverage on the D-day to teach our students and their parents some basic numerical properties—for example, conducting a recreational math session on “Number Theory 101” for secondary 1–4 (or grades 7–10) students might prove more meaningful or fruitful than dabbling in some numerological prestidigitation, or unhealthy divination.

**A Search for Patterns**

91 is the product of two primes: 91 = 7 × 13

**91 = 1² + 2² + 3² + 4² + 5² + 6²**

91 is also the sum of three squares: **1² + 3² + 9²**

*Are there other ways of writing the number 91 as a sum of squares?*

**91 = 3 ^{3} + 4^{3}**

**Non-Numerological Questions to Promote Problem-Solving Skills**

**Non-Numerological Questions to Promote Problem-Solving Skills**

Let’s look at an “inauspicious number” of elementary- and middle-school (primary 5–secondary 4) math questions, which could help promote numeracy rather than numerology among students and teachers.

**1. Sum of Integers**

Show that the number 91 may be represented as the sum of consecutive whole numbers. In how many ways can this be done?

**2. The Recurring Decimal**

What fraction represents the recurring decimal 0.919191…?

**3. Palindromic in Base n**

For what base(s) will the decimal number 91 be a *palindromic number *(a number that reads the same when its digits are reversed)? For example, 91 = 10101_{3}.

**4. The Billion Heartbeat**

Does a 91-year-lifespan last less or more than a billion heartbeats?

**5. Day of the Week**

Mr. Lee Kuan Yew (September 16, 1923–March 23, 2015) died on a Monday. Using the 28-year cycle of the Gregorian calendar, which day of the week was he born?

**6. One Equation, Two Variables**

If *x* and *y* are integers, how many solutions does the equation *x*² – *y*² = 91 have?

**7. Singapore’s New Orchid**

A new orchid—Singapore’s national flower—had been named after Mr. Lee: **Aranda Lee Kuan Yew**. Using the code A = *x*, B = *x* + 1, C = *x* + 2, …, , does there exist an integer *x* such that ARANDA sums up to 91? In other words, does there exist a numerological system such that A + R + A + N + D + A = 91?

**8. Singapore’s Coin Goes Octal**

There is an apocryphal story that had circulated for many years linking Mr. Lee Kuan Yew with Singapore’s octagonal one-dollar coin. A high-ranking monk had apparently told Mr. Lee that Singapore’s fortune would continue to rise only if Singaporeans were to carry a *bagua*—the eight-sided *fengshui* symbol. That prediction allegedly prompted the Monetary Authority of Singapore to issue the octagonal shape of the nation’s one-dollar coin.

That rumor was later put to rest by no other than self-declared agnostic Mr. Lee himself in one of his books, *Hard Truths*. He remarked that he had zero faith in horoscopes, much less the pseudoscience of fengshui.

What is the sum of the interior angles of the Singapore’s eight-sided coin?

**9.** Show that the largest number *k* for which the decimal expansion of 2* ^{k}* does not contain the digit 1 is 91.

© Yan Kow Cheong, April 26, 2015.

**Selected Answers/Hints**

**1.** One example is 91 = 1 + 2 + 3 +⋯+ 13.

**2.** 91/99.

**5.** Mr. Lee was born on a Sunday.

**6.*** Hint:* Show that x² – *y*² = 91 has 8 integer solutions.

**9.** *Hint*: Use a computer to verify the result.