Rabbit Math

Looking at the number of math questions that feature animals and birds, not even man’s best friend comes close to the rabbit—the beloved pet of math writers and teachers.

Think of the Fibonacci numbers, published by Leonardo of Pisa in Liber Abaci ("Book of the Abacus" or "Book of Calculating") in 1202, in connection with the rabbit population:

If every month a pair of rabbits produces one new pair, which begins to bear young two months after its own birth, how many pairs of rabbits will there be after a year?

Show that at the end of the twelfth month, there will be a dozen dozen pairs from a single pair.
  

An e-card I made before someecards banned users from designing their own. 

Why Singapore Math Loves Bunnies

Singapore math wouldn’t quite stand out from other foreign math curriculums, without its unhealthy number of brain-unfriendly math questions on chickens and rabbits (and goats and sheep). Even the smarter and (arguably) cleaner pigs unfairly lose out vis-à-vis the rabbits, simply because it's politically or religiously incorrect to use "infidel" pets or mammals and "haram" items in Singapore math textbooks, which are primarily targeted at a multiracial and multicultural student population. 

Through my dozen-odd supplementary Singapore math books, I'm guilty of contributing to the undue stress inflicted on millions of bunnies and their caring (or mathophobic?) owners around the globe. Below are two elementary math rabbit questions taken from my unpublished manuscripts:

A farmer has some chickens and rabbits. 

There are 60 eyes and 100 legs altogether. 

How many chickens and how many rabbits are there?

Since both chickens and rabbits each have 2 eyes, the total number of animals is 60 ÷ 2 = 30.

Suppose all 30 animals were chickens. Then there would be a total of 30 × 2 = 60 legs.

So the extra (100 – 60) = 40 legs must have come from the rabbits.

Each rabbit has (4 – 2) = 2 more legs than a chicken.

So there are 40 ÷ 2 = 20 rabbits and 30 – 20 = 10 chickens.

Challenge: Can you solve the above word problem, using a different method, say, the Stack Model Method, or the Sakamoto Method?

The next grade five or six question showcases two methods of solution, commonly used in Singapore local schools—students aren't expected to solve it by substitution or elimination methods, as these aren't formally taught in elementary school.

Guess Who's Suing Singapore?

A few years ago, I produced the bunny meme pictured below and posted it on the Imgur app, together with the accompanying wicked question:

Farmer Yan has almost twice as many chickens as rabbits. 

The total number of legs and heads is 184.

How many rabbits are there?

Now you know why these angry bunnies are "mathematically stressed," compared to the lazy, pampered cats and guinea pigs! Can you show why the answer is 17 rabbits? If as an elementary math student you could solve this, the odds that you might be born or blessed with the "mathematical gene" are pretty high.

Murderous Math—Let's Prey

In the wild, the rabbit is inarguably the most preyed-on animal in the world: from cobras, pythons, eagles, owls, lions, tigers, wolves, and hyenas, just to name a few common predators.

Guesstimate how many predators depend on the rabbits for their livelihoods every year. Or, how many rabbits have their lives cut short to feed their predators? Well, see these predators as playing their part in maintaining a healthy ecosystem for mankind—a proof that life isn't fair.

Political Rabbit Math

My childhood made-in-China candies

Recently, in the heat of the trade war between the US and China, as nationalistic mainland Chinese tried to promote their own brands of local products, I coined Rabbit Math and got it approved on Urban Dictionary, before some mean fellow probably with an axe to grind maniacally tried to continually downvote the phrase and had it taken down from cyberspace.

Beware of "digital terrorists" who just don't want to see even neutral mathematical terms or words floating on the internet—indeed, this sounds like the mathematical equivalent of Boko Haram.

One pair of rabbits can produce 60 babies a year.

Go Forth and Multiply

Before 1788, there were zero rabbits in Australia. That year, rabbits arrived on a boat from England; by 1950, there were 600-odd million rabbits in the Land of the Kangaroos.

If humans had babies at the rate rabbits do, show that our global population would double every three weeks. 

The Rabbit Habit

Early this year, I christened "5-Day Weekend" as a working template to promote creativity and productivity among time-poor workers, who always complain that their weekends are too short, and can't hardly get any productive work done on weekdays.

Rabbits by Numbers

Let me end with some tidbits about the idiosyncrasies of our beloved bunnies.

From: Mike Lowery’s “Random Illustrated Facts” (2017)

Those of you, who are bunny lovers, please share with the rest of us your favorite numerical factoids or numeroids about these cute animals.

As Productive as Fibonacci

Amateur-mathematician Fibonacci was a math popularizer and writer, who promoted the Hindu numerals during his European travels, besides blessing the mathematical brethren with a number of interesting or story arithmetic problems, one of which is the "rabbit problem" for which he's dearly remembered today. 

At a time when greying Singapore is historically experiencing its lowest fertility rate—which may lead the island-state to go the way of the dodo, if no disruptive measures are taken, other than conveniently (or simplistically?) depending on baby bonus incentives and immigration to arrest the population decline—for us, math educators, let's not stop being as mentally fertile and creative and productive as Dr. Fibonacci, although few of us would dare to promote the kind of productivity rate of his fertile bunnies!

Bibliography & References

Adam, F. (2014). The awesome book of awesomeness. London: Bloomsbury.

Fairbrass, M. & Tanguy, D. (2017). The scale of things. London: Quadrille Publishing Limited.

Lowery, M. (2017). Random illustrated facts. New York: Workman Publishing Co, Inc.

White Rabbit milk tea sells at 2,000% premium as Chinese consumers show support for local brands amid trade war http://bit.ly/2KPj43h

Yan, K. C. (2015). The stack model method: An intuitive and creative approach to solving word problems—Grades 5–6. Singapore: MathPlus Publishing.

Yan, K. C. (2015). The stack model method: An intuitive and creative approach to solving word problems—Grades 3–4. Singapore: MathPlus Publishing.

Yan. K. C. (2013). The chickens-and-rabbits problem. https://www.singaporemathplus.net/the-chickens-and-rabbits-problem/

© Yan Kow Cheong, July 30, 2019.

The Mathematics of 7Eleven®

The chain of 7–11 convenient stores is so called because these family-friendly outlets used to be open from 7:00 a.m. until midnight, but now they're open all the time in the least expected locations: 24/7/365. 

Other than munching and gulping at odd hours at 7Eleven stores, these franchise outlets also provide a fertile ground for math educators to come up with some creative math questions to enhance their students' mathematical problem-solving skills. Here are a sample of eleven non-routine elementary and middle-school math questions that may appeal to your students.

7-eleven.com

1. Number of Convenient Days 

In the U.K., 7/11 is abbreviated as 7th November; in the U.S., 7/11 is written as July 11. How many days are there from the U.S. date to the U.K. date?

2. The Recurring 711

What fraction represents the recurring (or repeating) decimal 0.711711711…?

3. The Day of the Week in 711 Days 

If 7/11 (July 11 in the United States) is a Friday, which day of the week was 7/11 in 2011? What day of the week will it be 711 days from now?

Source: Clipart ETC

4. The Acute Angle at 7:11

What is the angle between the minute hand and the hour hand at 7:11?

5. The Likeliest 7/11 Day of the Week

Which day of the week is 7/11 most likely to fall in a 400-year calendrical cycle?

6. Tangram-izing 7/11

Use three sets of the seven-piece Tangram to form the numerals 7 and 11.

7. Number Freaking 7/11

(a) Estimate the average revenue generated by all 7Eleven outlets in the United States every day.

(b) What land or area space is occupied by all 7/11 convenience stores in the world?

8. Are There 711 Digits or More?

How many digits do these indexed numbers have? (a) 7¹¹ (b) 7⁷¹¹

9. The 711th Digit Is…

What is the 711th digit of the decimal expansion in the reciprocal of 711?

10. 7Eleven Are Closed …

7Eleven outlets are open 24/7/365. However, on a few occasions some stores had to be closed. Suggest some possible reasons for the closure of these convenient outlets.

11. What Are the Prices in 7-11?

Mr. Yan went inside a 7–11 store and selected four items. When he reached the counter to pay for the goods, the cashier took his calculator, pressed a few buttons and said: "The total price is $7.11."

Mr. Yan replied, "Are you sure? Do I have to pay $7.11 because the name of your shop is 7–11?"

The half-embarrassed cashier answered, "Of course not! I've multiplied the prices of these four items and I've just given you the total."

The puzzled Mr. Yan laughed and said, "Why did you multiply these numbers? You'd have added them to get the total price!"

The cashier said, "I'm sorry; I've pressed the wrong button!"

The cashier then repeated all the calculations, by adding the prices of the four items, and to his surprise, the total was still $7.11.

What are the prices of these four items?

Selected Answers

1. 120 days

2. 79/111

3. (i) Monday (ii) Tuesday.

4. 149.5°

8. (ii) 601 digits

9. 9

10. $3.16, $1.25, $1.20, $1.50.

References

Michalewicz, Z. & Fogel, D. B. (2004). How to solve it: Modern heuristics. New York: Springer-Verlag.
Yan, K. C. (2011). Christmaths—A Singapore math creative problem solving title. Singapore: MathPlus Publishing.

© Yan Kow Cheong, July 11, 2014.


Postscript: This writer isn't sponsored in any way by the 7Eleven brand to write this blog article. However, he won't turn down any cash donations or vouchers, if his e-article has helped challenge and benefit tens of thousands of 7Eleven math fans around the world.