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!

Sneak Preview - Tile Puzzler

For anyone who is curious to see what is "in the works", here's your opportunity to see a game in the process of development. Take a look at Tile Puzzler - a new puzzle website hosted by The Problem Site

Tile Puzzler is similar to Quote Puzzler, in that it will offer a daily puzzle. Unlike Quote Puzzler, however, Tile Puzzler will not be offering word games, but a more geometric puzzle.

Tile Puzzler is based on the very familiar Pentomino shapes. But the site will also include some interesting variations, including puzzles with the Tetris pieces, as well as an advanced mode in which tiles are allowed to overlap under certain conditions.

Go ahead and stop by, check it out. At the moment of this writing, there is only one puzzle on the site. If you want to be notified when there site is fully operational, click the email link on the home page.

Enjoy!

Tile Puzzler