The number of cards in each Xovimat pack can be found in Pascal's triangle, a portion of which is shown below. Hyphens are left out of designators to save space; this leads to no ambiguity because in each of these examples the largest index is a single digit. The legends of nontrivial packs appear in black, red and blue:
Quantity of cards in nontrivial
pack
Designator of red
pack
Designator of blue pack
while trivial packs use green:
Quantity of cards in trivial
pack
Category: W, X, Y or Z
Here is the triangle itself:
1
W Z
1
W Y
1
X Z
1
W
2
X Y
1
Z
1
W
3
X
3
Y
1
Z
1
W
4
X
6
22
32
4
Y
1
Z
1
W
5
X
10
33
43
10
222
432
5
Y
1
Z
1
W
6
X
15
44
54
20
333
543
15
2222
5432
6
Y
1
Z
1
W
7
X
21
55
65
35
444
654
35
3333
6543
21
22222
65432
7
Y
1
Z
1
W
8
X
28
66
76
56
555
765
70
4444
7654
56
33333
76543
28
222222
765432
8
Y
1
Z
1
W
9
X
36
77
87
84
666
876
126
5555
8765
126
44444
87654
84
333333
876543
36
2222222
8765432
9
Y
1
Z
1
W
10
X
45
88
98
120
777
987
210
6666
9876
252
55555
98765
210
444444
987654
120
3333333
9876543
45
22222222
98765432
10
Y
1
Z
Trivial packs will probably not be useful, but here nonetheless is an explanation of their categories:
| Trivial category | Defining criterion | Examples | Quantity of cards in pack | Distinction between red and blue packs? |
|---|---|---|---|---|
| W | Valence = 0 | image | 1 | No |
| X | Valence = 1 | 14 (table or image) | Floor + 1 | No |
| Y | Floor = 1 | 1-1-1-1-1 (table or image) | Floor + 1 | Yes, unless valence < 2 |
| 5-4-3-2-1 (table or image) | ||||
| Z | Floor = 0 | 0-0-0-0-0 (table or image) | 1 | Yes, unless valence < 2 |
| 4-3-2-1-0 (table or image) |
Note that some very small packs fall into two trivial categories.
In category W the floor and ceiling of a pack are indefinite. Also, writing the designator for a pack in this category is difficult, because the designator contains no typographical characters.