18 Circles

The premise of the math game 18 Circles is to roll three eight-sided dice and then use addition and subtraction to manipulate the numbers into equaling one of the eighteen Number Circles that surround the scoresheet. At the same time, a player will be trying to form Straights using four or more numbers in a row placed in the inner Purple Ring of the scoresheet.

18 Circles was invented on July 13th, 2022. I had originally intended to make a number’s version of TRIPS, using eight-sided dice with numbers instead of colors. (TRIPS is a simple game for kids and may be found on the Paper Games section of this website.) After I started my preliminary design in Photoshop, however, the game gradually became a bit more complicated and I realized it would be more of a thinking game such as Square 36.

Writing the directions for a new game can be tedious at times. There is only so much that can be written strictly from imagination. The first time you actually start rolling the dice it soon becomes apparent that many changes are forthcoming. I’ve rewritten the rules over 6 or 7 times. 🙂


The following images show the progression of the game, which was originally named 1636, during a three day span starting July 13th thru July 16th, when the game was mostly finalized.

The first drawing is never very professional. But you have to start somewhere,
First structure created in Photoshop.
I needed to make it small enough to get two scoresheets on a page. Notice the zeros at the top and bottom of the circle.
My first attempt at playing the game. This is where the concept of making a Straight developed. I realized I needed another ring and the spokes needed a bit of rearranging.
At this stage the design was pretty close to being finished.
Final scoresheet 2025

18 Circles Rules and Directions


Click the image below for a PDF file that contains the complete Rules and Directions for 18 Circles. It is a big file and may take a few seconds to download. Included is a step by step analysis of a typical game of 18 Circles. This may help a person grasp the fundamentals quicker.

These two buttons will open reference sheets for playing 18 Circles. You can print them out and keep them together in a plastic sheet cover.

The button below will open an instruction/reference page. It may be helpful to print it out and place it in a plastic sheet protector for use during a game.


18 Circles Scoresheets

The image on the right is an 18 Circles scoresheet.

Click the image, save it to a hard drive, then print. It may be plasticoated for use with dry erase markers




To play 18 Circles you will need (3) eight-sided dice. I suggest buying some online; it is more fun to actually roll physical dice during the game. To play right away, however, click the link below. One six-sided die will appear. Click on it and it will disappear. Now click on the Purple 8 three times.

Roll and Go!

Google Dice Roller

The last time I called the dice up and then rolled them. TRIPS! 🙂



This is a great way to carry dice and shake them up while on a plane, train, boat…..or watching tv!

Click the square button to watch full screen.

This is an actual game played in the Tampa Airport while waiting for a flight during a thunderstorm.

High score so far!
8-12-22 65 points


18 Circles? Nope, just 1