Perfect-N Chart Generation

This page generates Perfect-N and Complementary Perfect-N racing charts.

For most common racing needs, you may be better served by the "Partial Perfect-N Chart Generator" which produces the most useful Perfect-N and Complimentary Perfect-N charts and fills in the many gaps (where no Perfect-N charts exist for this many cars) with Partial Perfect-N charts.

To produce a chart, choose a track size, select some options (check boxes and combo boxes) and "push" the chart's "button". Each button is labeled with the chart's name.

Perfect-N and Complementary Perfect-N Charts...

Perfect N charts satisfy the criteria that each car races in each lane the same number of times, and each car races every other car the same number of times.
Complementary Perfect N charts satisfy the additional condition that every race between two cars is matched by a corresponding race in which the cars reverse lanes.

Scoring Grid...
Selection of this option provides a score keeping grid in which each racer's scores can be recorded in the column under the racer's number. This grid is only produced for "smaller" charts, since it's width rapidly "gets out of hand."
With this option, "Total Score" and "Finish Place" lines are also provided.
Scoring grids are only provided when the number of cars plus the number of lanes is less than 20.

Chart Ordering...
If you clear all three of the ordering check boxes, then you'll get the orderings provided by the generators. Many of the generated chart sections will always have at least one car in every pair of consecutive races.
The more rules you enforce, the longer it will take your chart to generate. Depending on your browser (MSIE is faster than Netscape at reordering) you may have to wait quite a while for the larger charts.
For example the Complementary-Perfect 21-5 (2) chart (42 heats) with full optimization required 24 seconds to generate on a 75MHz Pentium running Windows 3.11 and Internet Explorer (MSIE).

Usage Notes...

With Netscape Communicator 4.01, I am unable to print or to resize the resulting windows. In both situations, the generated window reverts to the content of the original window. We think that this is a bug in Netscape. Perhaps this is a throwback to a similar limitation in Netscape Navigator 2. If you have better information, it will be greatly appreciated.

In some implementations, such as MSIE with AOL 3 and Windows 3.11, there appears to be a size limitation on the produced page. With that browser, I can not display chart C-P 91-10 (2). However, Netscape Navigator 3 and Netscape Communicator 4 produce it correctly.

If you have success or failure generating charts with this page, I will be interested to know the browser and OS that you are using. Email to

For the mathematical underpinnings of these racing charts see Complimentary Perfect-N Racing Charts.

Latest update: 1/5/2000 Reference to Partial Perfect-N Chart Generator
First issue: 11/11/97
Copyright 1997, 1999 © by Stan Pope and Cory Young. All rights reserved.