## Arithmetic Complexity

Arithmetic complexity shows the variations of differences between the numbers of analyzed tickets. The formulae is:

Arithmetic Complexity(t) = D(t) - (r-1)

where D(t) is the count of unique differences between all ticket numbers and r is the count of numbers in the analyzed ticket.

In a 6/xx lottery the Arithmetic Complexity value ranges from 0 to 10. About 74% of all possible combinations have the Arithmetic Complexity value in the range of 8 to 10.

### Example

Let's analyze ticket 1-2-3-4-5-6. The differences between all ticket numbers are:

2-1 = 1
3-1 = 2
4-1 = 3
5-1 = 4
6-1 = 5
3-2 = 1
4-2 = 2
5-2 = 3
6-2 = 4
4-3 = 1
5-3 = 2
6-3 = 3
5-4 = 1
6-4 = 2
6-5 = 1

There are 5 unique differences: 1, 2, 3, 4, 5 so the Arithmetic Complexity of this ticket is 5-(6-1) = 0

The same analysis of ticket 1-2-4-8-13-21 shows the following differences:

2-1 = 1
4-1 = 3
8-1 = 7
13-1 = 12
21-1 = 20
4-2 = 2
8-2 = 6
13-2 = 11
21-2 = 19
8-4 = 4
13-4 = 9
21-4 = 17
13-8 = 5
21-8 = 13
21-13 = 8

None of the differences above repeat so there are 15 unique differences so the Arithmetic Complexity of this ticket is 15-(6-1)=10

These statistics are available in summary form and also as per-ticket properties.