yyGrams is the puzzle you construct yourself without software or handheld device, to any imaginable difficulty. You don't need the answer beforehand.

No numbers to arrange, no words to spell or search out; just general troubleshooting logic skills


yyGrams   the troubleshooting puzzles
and yyRaptor logo yyRaptor online

What are these puzzles about?
What is a yyGram™?
What does a solution look like?
How do you make a yyGrams™ puzzle?
How do you solve a yyGrams™ puzzle?
What can you say in a yy-gram?
How do you say things in a yy-gram?

What are yyGrams puzzles about?

They are about skeletal logic—logic considered apart from any particular context—purely formally.

What is a yy-gram?

A yy-gram is an arrangement of enclosers—containers. Two special yy-grams are called simple. The yy-gram yin consists of nothing at all.

The other simple yy-gram, yang, consists of an empty enclosure, ( ).

Non-simple yy-grams may contain names and enclosures. Both may be enclosed to any depth. A name may appear any number of times in a yy-gram. A name may appear outside all enclosures.


What does a solution look like?

b.1 A solution, both in the puzzle and in the yyRaptor game, is a yy-gram. You will see in course that a yy-gram that fits the puzzle just below is ((f)(b)). An equivalent yy-gram is ((b)(f)), because serial order doesn't matter in zang-fu disappearance. Only inside-outside matters.

Here are three more example yy-grams:


((f)g m)

d (f m)(a f)


How do you make a yyGrams puzzle?

b.3 Throw together a value outcome catalog in two parts: a yang-outcome-list and a yin-outcome-list and you have a yyGrams puzzle.

An outcome-list is a list of there-lists. Example of outcome-list:

<n: { } {b} {f} >.

The there-lists in the outcome catalog tell how names are to be substituted in a yy-gram.

This outcome-list is tagged n:, for "yin," or "no, nothing there."


b.5 This one gives three there-lists that come out yiN.

{ } says to substitute yiN for all names. That's the same as simply removing them from the yy-gram. After substituting and discarding, reduce the yy-gram by zangfu Good Luck to find the outcome.

{b} says to substitute Yang for b and discard all other names from the yy-gram. Substitute-and-discard constitutes valuation. After valuating, reduce the yy-gram by zangfu Good Luck.

{f} says to substitute Yang for f and discard all other names from the yy-gram. Then reduce by zangfu Good Luck to find the outcome.

b.7 Another example of outcome-list, this time a y-outcome-list: <y: {f,b} >. This outcome-list is tagged y:, for "yang," or "yes, something there."

In yyGrams puzzles, only one-letter names are used in there-lists and yy-grams.

b.9 Going by the outcome catalog, then, the puzzle just above is saying "make a yy-gram that comes out ( ) only when f AND b are both there."


How do you solve a yyGrams puzzle?

d.1 On this site there are plenty of worked examples showing how to go about solving a yyGrams puzzle. When you need more, do a Twitter search on "#yypuz" to find people to trade puzzles and "#yygram" answers with.

d.2 Tweeted puzzles whose ID starts with "dzeth" (probably from me—@yyGrams)  all have matching "#yygram" answer tweets.


i.0 Say What?   Logical Relations

Comboo relations (combinatoric-boolean)

The main comboo relations are NOT, AND, OR, IMPLIES (if-then). The rest are built from these.



The quantifiers are SOME, ALL, NO (none of), there EXISTS. They are built from the comboo relations.

Logic involving time sequence—BEFORE, AFTER, WHILE, ...—has a separate vocabulary, not directly in the yy-gram (zang-fu disappearance, pancake, box arithmetic) vocabulary.


Yes-no, true-false, there-absent, ON-OFF, and so on, are paired values involved in logic. In zang-fu, the paired values are yang and yin, symbolized by ( ) and nothing.


i.1 Say How?

Expressing logical relations as yy-grams:


Combinatoric relations (boolean; propositional logic)—the "comboo vocabulary"

negation   NOT a :                                 (a)

conjunction   c AND d AND e :                 ((c)(d)(e))

disjunction       a OR b OR f :                 a b f

exclusive-OR     q XOR s XOR t :             ((q)s t) (q(s) t) (q s(t))

implication       IF p THEN q :           (p)q

          one form
    u IFF w :             (((u)w) ((w)u))mutual implication,
the AND of reciprocal implications


          another form
    u EQU w :       ((u)(w)) (u w)both-or-neither

Existential quantification (predicate logic; existential logic)

existence   THERE IS SOME u :       u

That is, putting a name of a class (set, entity, ...) explicitly into a zang-fu milieu is a claim that at least one member of the class exists: "There is such a thing as a unicorn." (Existence by co-ordinate mention theorem, Zethmayr)

i.2 Keeping the "comboo" vocabulary in mind will be a big help as you analyze outcome-lists.


i.3 Much robotics logic involves time, with relations such as before, during, after, while, until. yy-grams do not directly express time relations. However, time relations and their information sources can be named. Since yy-grams handle names with yes-no values, time relations can be handled within yy-grams.



zang good luck: (( ))=    

fu good luck: ( )( )=( )

There-list (substitution list; valuation)

gt.1 — Names in a there-list are replaced in the yy-gram with yang, ( ). All other variables in the yy-gram are removed for that valuation. Then the yy-gram is evaluated by zang-fu good luck chops.

Variables in a there-list not appearing in the yy-gram are simply ignored.


The "Puzzle Passport" tutorial here gives more examples.

Puzzle Passport, onscreen layout     .pdf 6.6K
Puzzle Passport, print layout     .pdf 5.6K
Passport Cover     .pdf 4.9K



yyGrams is also supplied in weekly feature layout, .pdf (Acrobat Reader) very small files, from PostScript handcode.

Sample#1       Sample#2       Sample#3


Puzzle examples of varying difficulty are out there in Twitter space. You don't need to have a Twitter identity or follow @yygrams to see them.

Twitter accommodates non-registered users. You can search for just yyGrams™ puzzles on the hashtag #yypuz. If you want to see answers at the same time, search on #yypuz OR #yygram.


Key Troubleshooting Skills to Cultivate

— Forming a theory (a model)


— Forming a hypothesis (a guess)


— Seeing how a theory suggests hypotheses

— Seeing ways to test a hypothesis in "what-if" questions

— Observing without panic

— Letting go of a hypothesis or a theory once it contradicts a solid observation

— Using negative information

— Having a few "next questions" in mind

Troubleshooting Attitudes

— Treasuring failures for what they taught you

— Treasuring "next questions" like Dylan Thomas treasures words

— Treasuring good problems no less than good answers

— Fleeing any company where a form of speech is outlawed (such as "problem").

(Toyota is not the only speech-police company.)

Without theory there is no learning. — Deming


©2012 David Zethmayr
2012.4.19 = 12h3   -   11:50J