Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping Game: Defined-Fixed, Balanced.

This game has a Linear structure paired with four Grouping rules. Because there are two dogs placed each day, our diagram will feature the days as the base, with two spaces per day:

pt44_o04_g2_1.png

The first two rules include one block and one not-block:

pt44_o04_g2_2.png

Since these two rules address four of the six dogs in the game, what is the relationship between the two dogs—S and K—not included in these two rules? To determine this relationship, first analyze what happens when the blocks are placed (in this analysis, disregard the linear aspect of the game and just consider the groups).


1. L and P must occupy one entire day:

pt44_o04_g2_3.png

2. G and H cannot be placed on the same day, and since there are only two days open, G and H must form a dual- option that occupies one space on each day:

pt44_o04_g2_4.png

3. By Hurdling the Uncertainty, we can infer that the two remaining variables, K and S, can never be placed on the same day:

pt44_o04_g2_5.png

Consequently, we can infer that S and K form a not-block:

pt44_o04_g2_6.png

This inference is directly tested in question #8.

There are also two powerful conditional rules in the game:

pt44_o04_g2_7.png

Because these rules involve two separate days and they both involve the second rule, they ultimately result in a single solution to the game:

• The third rule. When K is placed on Monday, then G must be placed on Tuesday. The LP block must then be placed on Wednesday. Consequently, because G is on Tuesday, H must be placed on Monday. The last remaining dog, S, must then be placed on Tuesday. Thus, when K is placed on Monday, there is only one solution to the game:
  
  
  pt44_o04_g2_8.png
  The fourth rule. When S is placed on Wednesday, then H must be placed on Tuesday. The LP block must then be placed on Monday. Consequently, because H is on Tuesday, G must be placed on Wednesday. The last remaining dog, K, must then be placed on Tuesday. Thus, when S is placed on Wednesday, there is only one solution to the game:
  
  
  pt44_o04_g2_9.png

The information above provides more than sufficient information to attack the questions, but a savvy test taker might suspect that given the powerful rules in this game, and the fact that there are no randoms, that there might be a limited number of solutions to this game. In fact, there are only eight solutions to the game, and these eight solutions can be captured using five templates. One option for attacking this game would be to show the templates, and in the interest of absolute clarity we will discuss how to make each template.

The basis for the templates is the placement of the LP block. Since the LP block can go on any of the three days, there are three basic avenues that lead to the templates:

LP on Monday:

When the LP block is placed on Monday, H and G must be split between Tuesday and Wednesday. However, the placement of S and K has an impact on G and H because of the action of the fourth rule. This ultimately creates two templates:

pt44_o04_g2_10.png

Template #1 contains two solutions; template #2 contains only one solution.

LP on Tuesday:

When the LP block is placed on Tuesday, both the third and fourth rules are affected: K cannot be placed on Monday, and S cannot be placed on Wednesday. Consequently, K must be placed on Wednesday and S must be placed on Monday. G and H form a dual-option that rotates between Monday and Wednesday:

pt44_o04_g2_11.png

This template contains two solutions.

LP on Wednesday:

When the LP block is placed on Wednesday, H and G must be split between Monday and Tuesday. However, the placement of S and K has an impact on G and H because of the action of the third rule. This ultimately creates two templates:

pt44_o04_g2_12.png

Template #4 contains two solutions; template #5 contains only one solution.

Either a regular setup or the template approach will effectively solve this game. In our explanations of the questions we will use the regular setup because more people attack the game using that method, and the template method still leaves several possible solutions undefined.

[schnappi]

Ignore the line on Monday. Didn't erase to save time. Game was moderately easy even though didn't make any deductions. Is anyone aware of any deductions at all in this game?

Realize now of course that the K cannot be on same day as S (question 2) but didn't make this "deduction" until tried four scenarios:
KG Tuesday doesn't work
HS,PL,KG works
H Tuesday, KS Wednesday doesn't work
GH,KS,LP doesn't work

44-3-2.jpg

[nicholaspavic]

Hi schnappi,

Again, this is a nice, initial set-up. You asked about inferences. Notice how with the first two rules, L and P taking up a whole day together with G and H on opposite days from one another and the LP block mean that K and S can now never go together. You actually could have inferred the K/S not block by thinking through the ramifications of the first two rules!

Of course, you caught yourself with second question and your testing of various scenarios but you probably want to really try to catch an inference like this after reading the first two rules. Because that is going to increase your speed and score. But overall, well done.

Keep up the good work!