Xovimat playing cards and Pascal's triangle.
Version of 2 November 2007.
Home

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 packDesignator of red packDesignator of blue pack

while trivial packs use green:

 Quantity of cards in trivial packCategory: W, X, Y or Z

Here is the triangle itself:

 1W Z 1W Y 1X Z 1W 2X Y 1Z 1W 3X 3Y 1Z 1W 4X 62232 4Y 1Z 1W 5X 103343 10222432 5Y 1Z 1W 6X 154454 20333543 1522225432 6Y 1Z 1W 7X 215565 35444654 3533336543 212222265432 7Y 1Z 1W 8X 286676 56555765 7044447654 563333376543 28222222765432 8Y 1Z 1W 9X 367787 84666876 12655558765 1264444487654 84333333876543 3622222228765432 9Y 1Z 1W 10X 458898 120777987 21066669876 2525555598765 210444444987654 12033333339876543 452222222298765432 10Y 1Z

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?
WValence = 0 image 1No
XValence = 1 14 (table or image) Floor + 1No
YFloor = 1 1-1-1-1-1 (table or image) Floor + 1Yes, unless valence < 2
5-4-3-2-1 (table or image)
ZFloor = 0 0-0-0-0-0 (table or image) 1Yes, 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.