yyGrams logoyyGrams > yyGrams logoworked > chop

zang: (( ))=    

shortstack disappears

fu: ( )( )=( )

extra Yang disappears

Technique: Expose Bogus Names

Bogus names in a yyGrams™ puzzle are there to distract and confuse your troubleshooting logic, so getting them out of sight is an early chore worth accomplishing.

This example focuses on technique of exposing bogus names.

We begin at the point where we have a complete outcome catalog listing, both the yin and yang columns, having reconstructed a missing column if necessary.

By a live range of 0-5 our puzzle author is telling us to expect any or all of the names in the pool to be bogus. No guarantees.

A non-appearing live range would mean the same.

<#yypuz 5>< abcde 0-5><y: { }{abe}{ae} {ad}{ab}{e}{b}{abde}{de} {abd}{a}{be}{bd}{d}{ade}{bde} ><n:*>auth BOGUS-BOG</yy>

—some unseen yy-gram—

yy col heads
—whole-pool catalog of outcomes—


{a,b,c,d}
{a,c}
{c,d}
{a,c,e}
{a,c,d}
{a,b,c}
{b,c,d}
{b,c}
{a,b,c,d,e}
{a,c,d,e}
{b,c,d,e}
{c,d,e}
{b,c,e}
{c,e}
{a,b,c,e}
{c}


{ }
{a,b,e}
{a,e}
{a,d}
{a,b}
{e}
{b}
{a,b,d,e}
{d,e}
{a,b,d}
{a}
{b,e}
{b,d}
{d}
{a,d,e}
{b,d,e}

The strategy will be to group the catalog into pairs of there-list valuations that differ by exactly one name, preserving, of course, their proper columns. If such a re-organization leaves no pairs straddling columns, the name we chose is bogus.

Inspect one of the outcome columns for a pair of valuations that differ by exactly one name. That name would be a candidate for bogus status.

Perhaps we spot, in the yin column, the pair {c,d}{a,c,d}, which differ exactly by a.

Re-order the catalog so as to pair up, where possible, all pairs that differ exactly by a. In a word, we call this operation "expose" a.

—some unseen yy-gram—

yy col heads
—re-order to expose a

{a,c}, {c}
{c,d}, {a,c,d}
{a,c,e}, {c,e}
{a,b,c}, {b,c}
{a,b,c,d}, {b,c,d}
{a,b,c,d,e}, {b,c,d,e}
{a,c,d,e}, {c,d,e}
{a,b,c,e}, {b,c,e}
---

{a}, { }
{a,b,e}, {b,e}
{a,e}, {e}
{a,d}, {d}
{a,b}, {b}
{a,b,d,e}, {b,d,e}
{a,d,e}, {d,e}
{a,b,d}, {b,d}
---

This differ-by-one pairing discloses that a never affects the outcome. Whether or not a is present, pairs stay in one column or the other.

Since a makes no difference ever, we clarify the catalog by dismissing all there-lists that mention a:

—some unseen yy-gram—

yy col heads
—re-catalog to dismiss a

{c}
{c,d}
{c,e}
{b,c}
{b,c,d}
{b,c,d,e}
{c,d,e}
{b,c,e}

{ }
{b,e}
{e}
{d}
{b}
{b,d,e}
{d,e}
{b,d}

We inspect again, always in one column or the other but staying in the same column, for a pair the differs by exactly one name.

Perhaps now we catch sight, in the yang ( ) column, the pair {b,e}—{e}, suspecting b. We re-order the catalog in pairs that differ exactly by b.

—some unseen yy-gram—

yy col heads
—re-catalog to expose b

{b,c,e}, {c,e}
{b,c}, {c}
{b,c,d}, {c,d}
{b,c,d,e}, {c,d,e}
---

{ }, {b}
{b,e}, {e}
{d}, {b,d}
{b,d,e}, {d,e}
---

Again we find no "straddlers"—all pairs are same-column pairs, meaning that the exposed name makes no difference in the zang-fu disappearance outcome.

Accordingly, we re-catalog to dismiss the exposed b:

—some unseen yy-gram—

yy col heads
—re-catalog to dismiss b

{c,e}
{c}
{c,d}
{c,d,e}

{ }
{e}
{d}
{d,e}

Now we spy, in the yin column, the pair {c,e}—{c}, differing exactly by e. We go through another "exposure" evolution:

—some unseen yy-gram—

yy col heads
—re-catalog to expose e

{c,e}, {c}
{c,d}, {c,d,e}
---

{ }, {e}
{d}, {d,e}
---

Again no "straddlers." The name e is exposed as bogus, so we can dismiss it in a further re-cataloging evolution:

—some unseen yy-gram—

yy col heads
—re-catalog to dismiss e

{c}
{c,d}

{ }
{d}

We may readily see on the clarified catalog that d stands exposed as bogus, failing to affect the outcome in every valuation case.

Let us dismiss d, then:

—some unseen yy-gram—

yy col heads
—re-catalog to dismiss e

{c}

{ }

The finally clarified catalog lets us state the necessary and sufficient condition for a Yang outcome on evaluation:

c  not there.


In formal logic terms this is said,

NOT c

The yy-gram that negates the yy-value of a name is an enclosure around the name:

(c)

The solution yy-gram might appear in tweet format as

<#yygram 5> <ans: (c) >auth BOGUS-BOG</yy>





Challenge for those really needing a mind-twist: construct an outcome catalog for a namepool-of-five such that all names are bogus.

Warning Label: the math teacher who was hired to construct all Bingo cards checked in at a mental hospital before finishing.

Better start with less than five...



©2012 David Zethmayr
2012.4.12 12gc:10:35J