The essential definition is the initial 5 x 5 grid which shows the analogous 'Chaturanga' pre-cursor of Chess moves of the different pieces from (X) center: S)hah, V)izier, F)ers, A)lfil, and the split symmetry of the Chess knight into 2 sets J)umper and L)eaper,

The second grid is the ordinal naming of the geometric dislplacement sets, an ideal mapping of alphabet 'Pachisi' alpha-numeric ordinals , the third is the perfect conventional BINGO array with 12 bold 'fixed' and 12 limited optional BC; EF&GH; JK; RS&TU; and the fourth grid is its corresponding "tabular" synchronicity.

The use of the alphabet is critical to understanding the system. The original concept of BOINxGSz requires the creation of the dummies by exchanging values, Right Side 'dummy' : tabular to FUNCTIONAL ( FUNCTIONAL from tabular) as well as the Left Side 'DUMMY': tabular from FUNCTIONAL ( FUNCTIONAL to tabular)

Substitutions are from an initial card of BINGO values, in other words between the [UPPER] case 3rd grid and the [lower] case 4th grid. The first level challenge puzzle: Given each dummy as a pair - can the 'source Bingo board be re-integrated? This is surprisingly simple, yet somehow elusive and tricky, the potential for error is considerable.

We have then the results showing each "dummy": one created from TABLE to GROUP (white values on black background) and its correlate from TABLE to GROUP (white on black) as "binary" tiles, a duality "duel" (hence du'e'lity). The first level objective is find the original BINGO board from which the binary tiling was derived -facilitated by the two composite board clues. This is only the beginning of a fascinating exploration....

Each dummy will now have new properties, but the RS dummy has the same alphabetical code - now if the same transmutation is continued a kind of Binary tree results. Intuitively I presume eventually it will be like a 'Mobius grid': everything will permutate back to source board...
(actually the LS dummy of first RS operation is in fact the source board - a similar result for RHS dummy of first LS operation does not.....)

The next phase is the random distribution of the integers 1 through 24, then assigning their numeric ALPHA designations from the 4 cardinal points of view: some will be in place - others will require either necessary or the 50/50 choices.The subtle factor remains that the assignment of the alphabetical functional sets can be permutated,in turn the tabulars once synchronized will permit the one to one substitution of BINGO numbers(or for that matter any distinct number groups, shapes, symbols, images,(words?, or even concepts?)

I have elaborated a system which extrapolates a particular type of Magic square - which has a specific relationship to certain underlying geometric principles. Hint: the 5x5 grid projects to a 9x9 grid with an inclusive even 8x8 grid. In turn there is a remarkable recursive property which is where the true gaming potential begins. One of the implied double 'entendres' in my choice of Bingo for Dummy's is that in a certain context rules of play are for Dummies e.g. the rules of Chess actually limit the potential of its concept - since simultaneous play is not possible!

Given that BINGO obviously DOES NOT require a manual to play; the need for a manual would imply that there is a body of data / detail to assist the player in taking up the challenge of creative/explorative play. There are some initial "puzzles" to be learned so as to enable further play - with the ultimate objective being to determine playable themes. The chief game potential to date lays the foundation for a simultaneous play game for 2 to 24 players, although this could also be seen in terms of 'n' players....

It consists of determining the scoring sequence from a random selection of one value from each distinct functional set - e.g VARIEM representing sets Vwyz Abcd Rstu Ijkl Efgh Mnpq - the choice of permutation left to players. From the represenation of the classic BINGO array the respective tabulars would be [ e - f - c - a - g - b ]This starting chain can now be extended into the full sequence which then is used as the order of moves, which in turn determines the vacated tile scoring order. This is ultimate challenge - an unusual environment where chance and skill can interface.

The principle of the original PACHISI (meaning 25), was an exploration of arithmetic properties which led to the discovery of zero. In turn this can be shown to relate to the special case Nasik Magic Square and its geometric principle of recursion, as being the quantum leap from arithmetic to geometric properties, (with its corollary trigonometric and algebraic features) the elements common to Chaturanga (quadripartite-division into four) the earliest known pre-cursor of Chess, which was clearly a 4-player game. ‘B’ 1-15; ‘I’ 16-30; ‘N’ 31-45; ‘G’ 46-60; the ‘O’ 61-75

Five random values are selected from each successive set of fifteen, but the central X is given no value there are only 4 selected. This ‘ideal average’ BINGO card has been divided into 4 geometric sets: 2 cardinal directions, blue & yellow; 2 sub-cardinal directions, green & orange, and a 5th set split into 2 approximate sub-sub-cardinal axes, violet & red. Chess players will recognize these as the two symmetries of the Knight’s move which are 4.065 degrees plus/minus the 1/16 divisions of a circle. Actually these five FUNCTIONAL sets represent displacement from the center which are the basic primordial movements of the earliest precursors of Chess. The BINGO numbers are Nominal numbers, in effect ‘named’ or identified as 24 values out 75 possible, having no significance in themselves. Any number of multiple sets of incremental (not necessarily sequential) values could be used.

The concept of ‘Ordinal’ or ‘ranking’ values of these cardinal value (nominals) is the critical feature which permits turning BINGO into an actual game/puzzle. Looking from the conventional South to North viewpoint the 5 random values from each successive column (West to East) may be ranked: ascending or descending.
By defining these as the Tabular ordinals (like a table of values), we can also view them as being isomorphic (one-on-one) within each of the six directional groups i.e. defining them as having corresponding Functional (geometric positioned) ordinal values.

To make this concept manageable an adaptation of the alphabet, excluding O&X (24 letters as in Greek alphabet) where the lower case letters are used for tabulars [t], and upper case letters for the functionals [F] is introduced to permit further exploration.

The initial random BINGO card used to generate successive pairs of clones: (each is a dummY) through a simultaneous exchange between the pairs of Functional &Tabular ordinal alpha-numeric values. The determination of the scoring sequence[s] in this BINGO-for-dummY’s allows for a surprising play challenge for 2 to ‘n’ players where imagination, mathematical skill, and judicial risk-taking form the solution approaches. It remains to discover if there are transferable real world applications related to finding the number of stages in its cycle where its extrapolation is analogous to the binary tree generation of ‘cellular automata’. An intriguing game theme is to further identify the synchronous patterns & sequences of the Ordinal sets which sum to the same perfect value – equal to 75.

The full development of the ‘bingo-for-dummY’s’ concept BGINSZ with a random scrambled BINGO card and the introduction of its 4 points-of-view. A special tiling set has been designed which leads to mosaics of melody, once the chromatic musical scale is introduced. The Harmonics become a portal to the ORIGINSZ © rt system of creative gaming using a universal language beyond words and the mumbo-jumbo of religions and political dogmas which may unite all peoples to share in a true universal experience of ‘order in space’

a B c d,

e f G h,

I j k l,

m N p q,

r S t u,

v w y Z

BINGO: under the ‘B’ five non-repeated values from the set 1-15; ‘I’ 16-30 ‘G’ 46-60 he ‘O’ 61-75 while under ‘N’ there are only 4 values out of 31-45 inclusive, since the central X has no value. The choice of 75 values may appear to be arbitrary, but not coincidental to the fact that a sum of numbers which total 75 are in fact of a particular mathematical significance. This ‘ideal average’ BINGO card has been divided into 4 geometric sets (blue, green,yellow,orange), and a split group of the 5th & 6th sets (violet & red), which Chess players may recognize as being the two symmetries of the Knight’s move [elL&Jay].The BINGO numbers are Nominal numbers, in effect ‘named’ or identified as 24 unique values out 75 possible, having no significance in themselves. Note that technically any number of multiple groupings of incremental (not necessarily sequential) values could be used. An argument could be made that the ordering of the files should correspond to the alphabetical sequence: hence BGINO as a little idea light goes on…there appears to be an interesting potential: B[O/X] ZINGS, also we might consider 4 points-of-view.

There are 24 counted numbers out of 75, each is a Cardinal value position. This nuance is readily understood within the context of ‘cardinal points’, the four principal directions, the compass ‘points’:North, East, South, and West. The Sub-Cardinal points are: North-East, North-West, South-West and South-East. Between the Cardinal and Sub-cardinal compass points are the Sub-Sub Cardinal points. Envision two symmetries (as if diagonals of squares equal to a circle’s diameter), the Clock-wise: North-north-east; East-south-east; South-south-west; West-north-west; and the Counter-clockwise points: North-north-west; West-south-west; South-south-east; East-north-east. Note that on the BINGO card, a 5x5 grid (tiling), there are 2 sets of Cardinal directions (blue & yellow) and 2 sets of Sub-Cardinal directions (green & orange) but that there are no ‘true’ Sub-sub Cardinal sets; the (Chess Knight) sets (violet & red) are 4.065 degrees ‘off’ from the 1/16 divisions of a circle. These Harmonics are the portal to ORIGINSZ © rt

The concept of ‘Ordinal’ or ‘ranking’ values of these cardinal value (nominals) is the critical feature which permits turning BINGO into an actual game/puzzle. Looking from the point-of-view convention of South to North the 5 random values from a choice of 15 in each successive column (from West to East) may be in either order – ascending, the conventional low to high, or descending. By defining them as the Tabular (like a table of values) ordinals, we can view them at the same time as being Functional (geometric positioned) ordinals corresponding to each of the six directional Cardinal groups in terms of their distance displacement from the center. To make this manageable a more practical adaptation of the alphabet, excluding O&X, i.e. 24 letters, (as in the Greek alphabet) is introduced in order to permit a further exploration of number which will lead us back to the properties employed to create Pachisi, (meaning 25), and subsequently Chaturanga (meaning quadripartite-division into four) the earliest known pre-cursor of Chess. In turn both can be related to the special case Nasik Magic Square and its geometric principle of recursion, the quantum leap from arithmetic to its geometric origins, and the corollary trigonometric and algebraic features, the elements which most likely led to the discovery of zero.

BI ZN GS © rt ( BOINGSZ, BINGZS, ZINGSBOX etc.) is the initial random scrambled BINGO card used to generate successive pairs of clones: through the simultaneous exchange between the Functional &Tabular ordinals. The determination of the scoring sequence[s] in this BINGO-for-dummY’s may be the world’s first play challenge for 2 to ‘n’ players where creative imagination, mathematical skill, and judicial risking of chance form the solution alternatives. It remains to discover if there are transferable real world applications related to finding the number of stages in its cycle: its binary extrapolation analogous to the tree root generation of ‘cellular automata’. Most intriguing as a game theme is to identify the patterns/sequences of the  Cardinal and Ordinal sets which sum to the same value - perfect solutions being equal to 75.

The key to this DUMMY is to recognize that the tabular ordering of successive columns (or files) is in terms of the functional (positional) ordering: the alpha ORDINALS, not the numbers themselves, whether the CARDINAL integers of a MAGIC SQUARE or any other structured array (even a random one!?) or the NOMINAL values in BINGO. (I used average values for ZINGSBOX puzzle). In effect this provides an insight to what was most likely the ‘origin’ of the gaming concept which was adopted to become the conventional ‘roulette on a grid’. The beautiful mathematics was probably not understood by the person or persons who introduced it – or it was ‘lost’ – all that survived was the one to one matching idea along ‘rows’ and diagonals (and other groupings).

This is the primer designed to become no less a popular pass-time and challenge than Sudoku, but unlike which is only the beginning of a voyage of discovery with extensions into Magic Squares, their recursion cycles, the connection to Chaturanga and the origin of Chess, all leading to the Master geometric model ORIGINSZ which I began developing in 1982.

Once upon a line, a point in time: a number, as a letter
marked its place in space,

but from its rigid viewpoint reached out to embrace a more universal reality.

As numbers come, so numbers go and some multiplied threefold

to stand like soldiers in a row doomed to become –BINGO –
why, and how did we fail

in our voyage of discovery where all is such perfect harmony?

But now let their inner truth be known and how magic springs:

BGINSZS… a child’s play game as the gateway to ORIGINSZ,

a geometric language by which to re-chart our mindscape

to challenge the twisted reason of this world

which cannot get its numbers straight

while its words are parsed to become absurd

as madmen plunder and destroy in their folly to claim God’s grace

The Divine Compass traces our ignoble fate:

Who will state Sum Ergo Cogito?

This puzzle is a (perfect) four points-of-view distribution, with a special 'universal' tiling of the average values used in BINGO (like in Bridge). From the standard position (of South looking North, columns East to West) what was the card of origin?
Hint: numerical values 1-24 are used for letters A-Z : where N=14 but skipping O, P=15, so that W=22 and skipping X, Y=23 Solution: Exchange functional alpha-numeric Ordinal values with their equivalent tabular values by substituting their corresponding Nominal(Cardinal) BINGO place value.

Test: ‘A F U N K Y’ Ordinals (of Cardinal Nominals) = 75 ; their Ordinal tabular (BINGO)Nominals = 228,
representing one quarter of their respective totals: 300 and 912 [950-38* center] average value of the “DUMMY”