Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Pattern Game

The game scenario is careful to stipulate that the strand of beads has only has a single direction, and thus the last bead on a strand is not next to the first bead. This is extremely important to understand otherwise you will make false inferences in some of the questions.

The first rule can be diagrammed as follows:

The first rule is quite valuable because it is a “space-eater,” meaning that it requires a lot of space to be enacted. When questions ask you to extrapolate out along the strand, this rule should be the first to be examined.

The second rule establishes that the only block that can occur is with the green beads. All other color blocks are prohibited:

The third rule prohibits orange and red beads from being consecutive:

The final rule is easily misinterpreted. The rules states that any portion of the strand containing eight consecutive beads must include all colors. Thus, if a strand has 10 beads, then beads 1-8 must contain all colors, beads 2-9 must contain all colors, and beads 3-10 must contain all colors. Understanding this “portional” aspect of the rule is particularly useful on question #17.

Combining all of the above leads to the final setup of the game; note that there is no traditional linear diagram because there is no known number of beads in a strand:

[TigerJin]

What game type is this game? In this list: http://www.powerscore.com/gamesbible/ls ... ification/ you guys have it listed as a pattern game. But there are rules here about the placement of variables, so, I don't see how it could be a pattern game. Can you tell how it is a pattern game? Thanks.

[Dave Killoran]

Hi Tiger,

Thanks for the question! Let's talk about what we're seeing here and then if you have any questions, just let me know.

First, the presence of rules that address variables doesn't automatically disqualify a game from being a Pattern game. This is especially true because rules that address the general nature of a game, such as "Any applicant who is interviewed second receives a job offer" could easily be rewritten into something that includes variables, such as, "If A, B, C, D, or E are interviewed second..."

Second, the interesting thing about Pattern games is that they have all been built on Linear games, so every Pattern game comes with a Linear designation as well. Thus, if you classify this as a Linear game, you aren't wrong in doing so. The value of the Pattern classification is that it tells you to look for something special in the way the rules work together and affect groups of variables and spaces within the game.

So, in looking at this game, we see the Linear element that has always been paired with Pattern games. The element that particularly jumps out to me as patternistic is the first rule, which dominates this game whenever it appears and which also takes up a huge chunk of space, limiting the possible outcomes. This rule, especially when combined with others, reduces what can occur and produces color orders that are limited and a bit predictable. So, while not nearly as precise as the pattern element in say, the Clan Game (December 1994, game #4) it still is in the same general area of ideas, and I chose to classify this as Pattern. But again, if you called it a Basic Linear game, it would not change how you would attack this game By the way, the reason this game ends up being more "open" than the normal Pattern games is that the number of spaces (in this case, beads on the thread) is not fixed. If we knew it was exactly 8 beads, that would limit the outcomes, but since we could have any number of beads, the game has more variations in play and that reduces the impact of the Pattern element here.

Please let me know if this helps. Thanks!

[TigerJin]

Interesting. I get it. Thanks!

[LetsGetThis180]

I'm having a little trouble breaking down the first rule. I keep rereading it like a hundred times. I know I have the other rules locked down.

My 1st rule looks something like this:

PY or YP RPYR or RYPR

Am I doing this correctly or somehow on the right track? It looks a little off to me. Maybe there's another way to write that rule? Thanks!

[Dave Killoran]

That's exactly what it is—good job!

[colguin27]

Hello,

I realized that I missed so many questions on this game because the explanations completely contradict the explanation for the December 2006 Game #3 (Rock Classics and New Composition) setup for the game. I am so concerned that I am missing something vital on my upcoming exam, OR that there is some sort of mistake. The December Game from 2006, claims that the first song CANNOT be a rock classic, because EVERY rock classic MUST be preceded by a new composition.

However, game #3 from PrepTest 20 claims that although if P and Y are adjacent they must be preceded and followed by a red bead, how is it possible for the first two beads to be purple and yellow respectively unless the strand is being twisted into a bracelet with the last one being red?

I feel like this is truly contradictory and not sure how to "resolve the paradox" here so I can get better scores on future games!

Thank you for your time,

-C

[Adam Tyson]

I had that same confusion at first, colguin27, so you aren't alone! However, the key difference is that the PY rule in this game isn't so absolute as to say that the PY block must be bracketed by red on both sides. Rather, it says that ANY bead that immediately follows or immediately precedes that pair must be red. That leaves open the possibility that there is NO bead that precedes or follows the pair! For example, the strand could be just two beads, P and Y in either order, and that would not break the rule because in that case there is NO bead that immediately follows or immediately precedes them. Read that "any" as the sufficient condition indicator that it is and you get a different sense of the rule. It's really saying this:

"If there is a PY or YP pair, and IF there is a bead immediately before that pair or immediately after that pair, then the bead or beads adjacent to the pair must be red."

Unlike the other game you cited, there doesn't HAVE to be another variable just before the pair, or another bead just after the pair. It's just that if there IS such a bead, it must be red!

(And I'll add this as an addendum to the exchange between Dave and LetsGetThis earlier in this thread - it's not really requiring an RPYR or RYPR block, because we could either start the strand or end it with a PY or YP pair.)

Confusing stuff, to be sure! I almost fell for it myself the first time and eliminated answer C from the list question.

[Zarie Blackburn]

We recently received the following question from a student. An LSAT Expert will respond below. Thanks!

I realized that I missed so many questions on the Bead Strand game from the Official PrepTest 20 because a principle in the setup completely contradicts the setup for the December 2006 Game #3 (Rock Classics and New Composition). I am so concerned that I am missing something that will be vital on my upcoming exam, OR that there is some sort of mistake or inconsistency. The December Game from 2006, claims that the first song CANNOT be a rock classic, because EVERY rock classic MUST be preceded by a new composition.

However, game #3 from PrepTest 20 claims that although if P and Y are adjacent they must be preceded and followed by a red bead, how is it possible for the first two beads to be purple and yellow respectively unless the strand is being twisted into a bracelet with the last one being red?

Please help me to "resolve the paradox" here so I can get better scores on future games!

[KelseyWoods]

An interesting question that requires a close read of these two rules!

The relevant rule in the December 1996 Game #3 is:
"Each rock classic is immediately preceded on the CD by a new composition."

Notice that this rule says that each rock classic is immediately preceded by a new composition. That means that every time you have a rock classic, it has to have a new composition right before it. Thus, a rock classic cannot be first, because it would be unable to have a new composition before it.

The rule from the October 1996 Game #3 is slightly different:
"If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red."

Notice that this rule doesn't actually say that a red bead has to precede or follow a PY adjacent pair. Rather it's saying that if there's a bead before or after that pair, then that bead must be red. If P and Y are 1 and 2, then there isn't a bead preceding that pair. So we don't have to worry about the "any bead that immediately precedes that pair must be red" part of the rule. But there is a bead immediately following that pair, and so that bead must be red.

It's a confusing rule because it kind of nests a conditional within a conditional. You could diagram it like this:

PY or YP [bead immediately before or after PY or YP red]

So it's IF P and Y are adjacent and IF there's a bead before or after them, THEN that bead before or after them is red.

Hope this helps!

Best,
Kelsey