Triangular Numbers, Square Numbers, and Rickie Puzzlers

Play A Rickie Puzzler!

What is a Rickie Puzzler? Well, to explain a Rickie Puzzler, you need to know what Triangular Numbers and Square Numbers are. Most people are familiar with square numbers: 1, 4, 9, 16, etc. These are numbers which can be obtained by multiplying a number by itself (5 x 5 = 25, for example, so 25 is a square number). Visually, a square number can be pictured as an array that is n units in width and n units in height.

So what's a triangular number?

The best way to think of a triangular number is to picture a top view of a set of bowling pins. They form a triangle. And there are ten pins. Ten is a triangular number. As you look at the pins, you'll see that the first row of pins has one pin, the second row has two pins, the third row has three pins, and the fourth row has four pins. 1 + 2 + 3 + 4 = 10.

From this, you can probably guess that triangular numbers are formed by adding all the positive integers from 1 to n. Thus 1, 3, 6, 10, 15, 21... are all triangular numbers.

Rickie Chase was exploring these numbers when it occurred to him that some triangular numbers are also square numbers. The number one is an example, although you might not think it's a very interesting one. Then we've got the number 36.

36 = 6 x 6, so it's a square number.
36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8, so it's a triangular number.

So Rickie began thinking: "I could build puzzle shapes containing 1, 2, 3, 4, 5, 6, 7, and 8 squares, and there would be a total of 36 squares. That means, if I made my pieces just right, I could fit them into a six by six square!"

And thus the first Rickie Puzzler was born. At the top of this blog entry you will find an example of a Rickie Puzzler. Here is another:



If you visit Tile Puzzler, you can find several Rickie Puzzlers. If you want to try solving a Rickie Puzzler, click the Puzzler By Number link, and then enter any of the following puzzle numbers: 48, 49, 50, 51, 53, 55, 62, or 64.

If you would like to build a Rickie Puzzler, it turns out that building one is as much fun as solving them. Just click the Build Puzzles link, and choose the "FreeStyle" option.

Once you've finished creating the Rickie Puzzler, click save. Once your puzzle has been added to the site, you'll be given the Puzzle ID number, so you can give it to your friends and challenge them to solve it!

Enjoy!