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.

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.

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