Mathematical Quickies and Trickies

What are mathematical quickies and trickies? Are they the so-called trick or tricky or IQ questions in mathematics?

mathematical quickie is a problem which may be solved by laborious methods, but which with proper insight may be disposed of quickly. This term was coined by Professor Charles W. Trigg to describe problems that yield almost instantly to a flash of inspiration.

mathematical trickie is a problem whose solution rests on some key word, phrase, or idea rather than on a mathematical routine. Most number riddles would qualify as trickies.

What Are Mathematical Quickies and Trickies?

● Questions teachers shy away because they are hard to crack if improperly approached. Conventional methods are seldom necessary to solve them; most are rather tackled in a common-sensical and logical approach.

● Questions or variations commonly set in IQ and aptitude tests to trap the unwary. They are what teachers called the “Tricky Questions.”

● Questions that may be solved by a bright 8-year-old child, yet defeat the average mathematics teacher and educated parent.

● Questions that defy intuition, frequently posed in math contests and examination papers to frustrate the rote learner and catch the mathematically challenged.

● Questions whose obvious solution is never the correct one—what offhand appears to be true is false.

Mathematical Quickies and Trickies will not only enhance your problem-solving skills, but also help you to be more careful in approaching unorthodox mathematics questions.

Once you’re familiar with these trick and tricky questions, the solutions of many of these non-routine questions will make them appear predictable, rather than challenging. What may, at first, appear challenging will, in the end, become routine.

All that you need is a little knowledge of elementary school mathematics, open-mindedness, and persistence to participate in the delights of Quickies and Trickies.

Let’s revisit some old-time mathematical quickies—they’re also some of my favorites.

0. A bottle of wine cost \$10.
The wine was \$9 more than the bottle.
How much did the wine cost?

1. The side of a square is increased by 30%. Find the percentage increase in the area.

2. If 3% of births produce twins. What percentage of the population is a twin: 3%, less than 3%, or more than 3%?

3. In a kilometer race A beats B by 20 meters, and he beats C by 40 meters. By how much could B beat C in a kilometer race?

4. Mrs. Goon’s children are all schooling, and the product of their ages is 45,045. How many children does Mrs. Goon have?

5. If I write all the whole numbers from 1 to 500 in a row, how many digits will there be?

Although there exist thousands of these quickies and trickies in the recreational mathematics literature, many of them require a fairly sophisticated level of mathematics from the problem solver.

To expose both upper primary and lower secondary school (grades 5-8) students to some of these entertaining non-routine questions, and to arouse their interests, Mathematical Quickies and Trickies contains over 300 elementary quickies and trickies, compiled from the fields of arithmetic, geometry, algebra, and recreational mathematics.

Ranging from the simple and trivial to the complex and challenging, most of these problems and solutions should prove accessible to the average primary (or elementary) school student. However, some of these trick and tricky problems may pose a challenge even to the talented or gifted secondary student.

The challenge of mathematical quickies & trickies is not only to solve these mathematical brainteasers, but also to come up with more elegant solutions than the ones provided.

References
Yan, K. C. (2012). Mathematical quickies & trickies. Singapore: MathPlus Publishing.
Yan, K. C. (2012). More mathematical quickies & trickies. Singapore: MathPlus Publishing.

© Yan Kow Cheong, June 7, 2014.

Trick and Tricky Math Questions

The sequel to the bestselling Mathematical Quickies & Trickies—Suitable for grades 5-8 students

What is the difference between “trick questions” and “tricky questions” in mathematics? Can you spot them to avoid being fooled by them?

Trick Questions

“Trick” questions are difficult because they often conceal or omit information, or because information appears in an unfamiliar setting. Trick questions are set to mislead the unwary — the novice problem solvers.

Trick questions often disguise themselves in the form of riddles and conundrums. Let’s look at two examples of trick questions.

Example 1
Joe cycles from home to school, a distance of 2 kilometers. If he cycles the first kilometer at 5 km/h, how fast will he have to cycle the next kilometer to average 10 km/h?

Example 2
As I was going to Mathland
I met a man with seven wives.
How many in all were going to Mathland?

Did you get 15 km/h as the first answer, and 2803 as the second answer? If yes, welcome to the company of trick-allergic people. Don’t give up so easily. Look at the questions again. Figure out why the two answers are wrong. Resist the temptation to peep at the hints.

Tricky Questions

“Tricky” questions are “fair”; they don’t usually conceal information or depend on some words, which may be misinterpreted. In fact, tricky questions often contain redundant information, which needs to be filtered.

Trickies are problems whose numerical data make the problem meaningless — unrealistic problems. The sensibility of the answers serves as a guide to warn the problem solver that the question may contain redundant or insufficient information. An experienced problem solver will notice the unreality or impossibility of the problem’s specific data.

Here are two “tricky” questions.

Example 3
Write, in algebraic form, the general form of numbers that, when divided by 3, leave a remainder of 5.

Example 4
The perimeter of a right triangle is equal to 3.92 m. Two of its sides are 1.25 m each. Find the third side.

Did you get 3n + 5 and 1.42 m? Or, are you more tricky-sensiive this time? What are the correct answers to these mathematical trickies?

May I direct you to the Mathematical Quickies & Trickies Fan Page for more trick and tricky questions in elementary school mathematics? Or, you may order some titles under the Mathematical Quickies & Trickies series at Amazon.com or download a soft copy from iTunes.

Happy mathematical problem solving!

© Yan Kow Cheong, May 21 2014.

A bestseller in Singapore among grades 4-6 students