# "Perfect N" Chart Generation Example

## Selected item:

**Cars** |
**Heats** |
**Chart Symbol** |
**Generator(s)** |

**3 Lanes** |

7 | 14 | CP7-3 (2) | {1, 2} {6, 5} |

## Chart Generation Steps:

### Step 1:

Note N, the number of cars; H, the number of heats; L, the number of lanes; and G(i), the generators for the selected chart.
N is 7 cars

L is 3 lanes

H is 14 heats

the Generators are {1, 2} and {6, 5}.

### Step 2:

Draw a grid of L columns and H rows.

**Lane** 1 |
**Lane** 2 |
**Lane** 3 |
**Generator** |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

-- | -- | -- |

### Step 3:

Enter the numbers 1, 2, 3, ... down column 1. If a result is greater than N, subtract N from it. Continue until column 1 is full. (The number in the last row should be N. If it isn't then there has been an error.)

**Lane** 1 |
**Lane** 2 |
**Lane** 3 |

1 | -- | -- |

2 | -- | -- |

3 | -- | -- |

4 | -- | -- |

5 | -- | -- |

6 | -- | -- |

7 | -- | -- |

1 | -- | -- |

2 | -- | -- |

3 | -- | -- |

4 | -- | -- |

5 | -- | -- |

6 | -- | -- |

7 | -- | -- |

### Step 4:

Next to each row that has a "1" in column 1, write one of the generators. Each generator should be used once. If not, then there has been an error.

**Lane** 1 |
**Lane** 2 |
**Lane** 3 |
**Generator** |

1 | -- | -- | {1, 2} |

2 | -- | -- |

3 | -- | -- |

4 | -- | -- |

5 | -- | -- |

6 | -- | -- |

7 | -- | -- |

1 | -- | -- | {6, 5} |

2 | -- | -- |

3 | -- | -- |

4 | -- | -- |

5 | -- | -- |

6 | -- | -- |

7 | -- | -- |

### Step 5:

In the following addition, if a result is greater than N, subtract N from it to produce a number in the range 1 thru N.
Apply each generator to fill in the remainder of it's row: Add the first number in the gernerator to the contents of the first column to produce a value for the second column. Add that number to the second number in the generator to produce a value for the third column. Continue in that fashion until all of the generator values have been used and each of the columns of the row have been filled. (It should come out even...if not, there has been an error.)

**Lane** 1 |
**Lane** 2 |
**Lane** 3 |
**Generator** |

1 | 2 | 4 | {1, 2} |

2 | -- | -- |

3 | -- | -- |

4 | -- | -- |

5 | -- | -- |

6 | -- | -- |

7 | -- | -- |

1 | 7 | 5 | {6, 5} |

2 | -- | -- |

3 | -- | -- |

4 | -- | -- |

5 | -- | -- |

6 | -- | -- |

7 | -- | -- |

### Step 6:

Fill in the remainder of each column by numbering sequentially down the column, beginning with the values already present. The next number after N is "1". Here again, if the number you are about to enter is larger than N, subtract N from it.

**Lane** 1 |
**Lane** 2 |
**Lane** 3 |

1 | 2 | 4 |

2 | 3 | 5 |

3 | 4 | 6 |

4 | 5 | 7 |

5 | 6 | 1 |

6 | 7 | 2 |

7 | 1 | 3 |

1 | 7 | 5 |

2 | 1 | 6 |

3 | 2 | 7 |

4 | 3 | 1 |

5 | 4 | 2 |

6 | 5 | 3 |

7 | 6 | 4 |

## Review

Note that since this was a "Complementary Perfect 7" chart, every match-up has a corresponding lane-swapped match-up. For instance, note that in the third row, car 3 is in lane 1 and car 6 is in lane 3. Down in the 13th row they are swapped... car 6 is in lane 1 and car 3 is in lane 3.
The places determined by racing this chart should be very accurate.

Back to the "Perfect N" Race Grid Directory

Back to the method page...

Latest update: 9/27/97

Copyright 1997 © by Stan Pope. All rights reserved.