Re: Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced, Identify the Templates game.

This game contains three variable sets: lanes, runners, and charities. The lanes should be chosen as the base since they have an inherent sense of order, and then the other two variable sets should be stacked above the lanes. This creates an Advanced Linear setup:

PT7-Feb 1993 LG Explanations game 4 setup diagram 1.png

The first rule is easy to address:

PT7-Feb 1993 LG Explanations game 4 setup diagram 2.png

The second rule creates a sizable block:

PT7-Feb 1993 LG Explanations game 4 setup diagram 3.png

Because K is already fourth, this block can only be assigned to lanes 1-3 or 3-5. Note that this placement automatically limits P to lane 2 or lane 4, and that lane 3 must be F or G (at this point).

The third rule creates another block, which has two possibilities that must be shown separately:

PT7-Feb 1993 LG Explanations game 4 setup diagram 4.png

Because K is already fourth, this block can only be assigned to lanes 1-4 (with G in lane 1) or 2-5.

The fourth rule is a simple sequential rule:

N > S

While we could take a moment and draw out the numerous Not Laws that follow from the rules above, a better approach is to examine the two blocks because they share a common variable: G. In fact, the two blocks can only be combined in two ways, creating two super-blocks that ultimately control the game:

PT7-Feb 1993 LG Explanations game 4 setup diagram 5.png

These two blocks represent the only possible combinations of the second and third rules (other combinations initially appear possible, but could not fit within the five-lane constraint imposed by the game). These two blocks are difficult to place, and with the additional rules that K is fourth and N > S, there can only be a limited number of solutions to the game. The best decision, then, is to diagram the templates that result from placing each block. In this case, the interaction of the blocks is so limiting that it produces only two basic solution paths for the game:

Template #1:

In this template, the super-block is placed in lanes 1-4. In the charities stack, only J and H are uncertain, and they rotate between lanes 2 and 5. In the runners stack, P and O are placed, and L, N, and S are unplaced. However, due to the fourth rule, S cannot be first, leaving a N/L dual-option, and N cannot be fifth, leaving a S/L dual-option. The only rule to track is the N > S rule.

PT7-Feb 1993 LG Explanations game 4 setup diagram 6.png

Template #2:

In this template, the super-block is placed in lanes 2-5. In the charities stack, only J and H are uncertain, and they rotate between lanes 1 and 2. In the runners stack, P and O are placed, and L, N, and S are unplaced. However, due to the fourth rule, S cannot be first, leaving a N/L dual-option, and N cannot be fifth, leaving a S/L dual-option. The only rule to track is the N > S rule.

PT7-Feb 1993 LG Explanations game 4 setup diagram 7.png

By identifying these two templates during the setup, the questions can be answered easily.

[Lance]

Hi,

I have been trying to work through this problem but keep running into difficulties answering the final 2 questions (23 & 24). I am not very confident in my set up for this question and any help in how to approach the game as a whole would be greatly appreciated.

The problem deals with five runners and five charities that represent each runner.

Thanks!

[WestDakota]

Hi Lance,

You've got a two-tiered linear game here, with unwieldy blocks that can only go in a limited number of configurations.

The second rule sets up a block with a total of six spaces: three on the top row (let's say that's the "runners" row); and three on the bottom (the "charities" row). P is in the middle space on the top row, and F and G occupy the corner spaces on the bottom row, except that you don't know what order F and G are in.

The third rule sets up an eight-space block (4 spaces on the top row and 4 on the bottom). Either it looks like O _ _ _ on the top and _ _ _ G on the bottom, or else it looks like _ _ _ O on the top and G _ _ _ on the bottom. Since you don't know what order O and G appear, it's best to just draw this block out both ways.

With the first rule, K is stuck in the 4th space of the bottom row. If you try to place the P/F/G block (second rule) with K taking up space, you'll see that you could only fit that block such that P is either space 2 or space 4. Combine this knowledge with what you know about G from the the O/G block (third rule), and you'll see there are only 2 ways of drawing the entire scenario:

Possibility 1:

1 2 3 4 5
_ O _ P _
_ _ F K G

Possibility 2:

1 2 3 4 5
_ P _ O _
G _ F K _

[hlg0035]

Hello! I'm having a ton of trouble setting up this game correctly. I have tried several different set ups but am not able to wrap my head around it. I have answered some of the questions but am specifically having trouble with question # 20, 23, and 24. Any help would be appreciated! Thanks!

-Hannah

[Jon Denning]

Hey Hannah - thanks for the question. Let me give you some tips on the setup, and then you can try out those questions again and see if they make more sense.

This is just an Advanced Linear game, where you'd want to use the lanes as a base, 1-5, and then have two spaces above each of the five lanes: one row for runners (LNOPS) and another for charities (FGHJK). At that point you could begin to fill in inferences and restrictions based on the rules, as follows:

rule 1 - put K above 4 in the charity row

rule 2 - this is a split block of either FPG, or GPF. Note that this block is restricted because K in 4 means the F/G charities will either be 1 and 3, or 3 and 5. Meaning P (runner row) is either 2 or 4. At this point I quickly sketched two templates for the block being placed 123, and 345.

rule 3 - this rule actually combines with rule 2 a bit to narrow things down even further. If there are two lanes between G and O, consider what that would do to each of the two templates we just drew: in the template where P is 2, G would have to be 1 and O 4 (F is 3) because we need room to separate G and O; in the template with P in 4, G would have to be 5 with O in 2 (F is 3 again) so that G and O are separated by two spots. So in both templates we've got a lot filled it!

rule 4 - simple one here, just a sequence with N to the left of S. So not laws in both templates of S not 1, and N not 5. That means spot 1 is N/L, and spot 5 is S/L

To recap, template 1 has charity row with G1, F3, and K4, and runner row with P2 and O4 (not laws of not S1, not N5). Template 2 is charity row F3, K4, G5, and runner row O2 and P4 (not laws not S1, not N5).

Use those and try the questions again--should be pretty straightforward.

Thanks!

Jon

[hlg0035]

Beautiful! Thank you! Makes senses now

[yenisey]

I only set up the second template and answered all the questions correct. I didn't even realize that there was another way , template. Anyway just having one set up really saved me time

[Robert Carroll]

yenisey,

I ran through the game with that one template, and it looks like it did answer every question! However, the first template also works for the game. It's pure luck that only the second template was ever needed for the answers - it looks like no answer seems right in the second template and is only wrong because of the first template. But that's pure coincidence. Whenever you do templates, you have to make sure you do all of them. Here, it was just luck that it didn't make a difference - that's rare, and you can never depend on it! If an answer was true in the second template but NOT in the first, then it would SEEM correct for a Must Be True question, but not really be right - so that was the danger that could have occurred, and typically will happen for these games. I don't know why the test makers made only one template relevant to their answers, but they didn't need to do that, and I can remember situations where all templates are necessary. So be sure to find them all in the future.

Robert Carroll