Another unforgettable problem is the following problem from the Canadian Mathematical Olympiad in 1989. Although I did not participate in that year's competition, I came across it as I was preparing for the competition in subsequent years. It is memorable not only because the problem is elegant but also from the personal connection with the …
My favourite card game is cribbage. I have played online for over 20 years. While it is not as well-known as other card games such as bridge or gin rummy or euchre, I enjoy the game for its combination of strategies, application of basic probability theory and psychology. Of course, as with many other card …
I am planning to start a series of unforgettable mathematical problems that I have encountered in my life. First of all, what makes a mathematical problem unforgettable? This of course is a subjective question. Usually, it is a combination of personal factors and elegance of the problem itself. This is the first of of these …
One of the first tricks taught in factoring polynomials is the difference of squares formula, namely: This simple formula comes in handy in mental arithmetic when we substitute and with numbers, especially when you have your square numbers memorized. For example, suppose someone asks you to calculate 27 X 23. Here's a quick …
This post is inspired by the well-known Christmas song "The Twelve Days of Christmas", which starts as follows: "On the first day of Christmas, my true love gave to me A partridge in a pear tree. On the second day of Christmas, my true love gave to me Two turtle doves, And a partridge in …
I introduced modular arithmetic in an earlier post (Introducing Modular Arithmetic via Group Theory). Let us look an application of this theory in the following problem. Problem: Prove that there are no perfect squares ending in 99. On the surface, this seems incredibly hopeless. After all, there are infinitely many number like this: 99, 199, …
1) I might be severely in debt but on a positive note, I have as much money as Elon Musk in absolute value. 2) Elon Musk's bank account balance has many digits. Mine has as many digits too, though they are after the decimal point.
I had the fortune to watch this play with my family. Without spoiling the play for people who have watched it, I want to pose a central question raised by the play. If you have a time-turner that can go back in time and change a few things in your life, do you want to …
Mdoular arithmetic is essentially arithmetic on remainders. Recall that whenever we have two integers , with , there exist unique integers and , with such that The number is the remainder. Doing arithmetic on remainders is usually much easier than doing arithmetic on the original numbers, especially if is small. In addition, since the set …
The Pythagorean Theorem is of course a well-known theorem. Basically, it states that the sum of squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. There are many proofs of this. The following is perhaps my favourite. Consider the diagram below: …
