Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Advanced Linear: Unbalanced: Underfunded, Identify the Templates game.

The game scenario establishes that on each of seven consecutive days, a pet shop features one of three breeds of kitten, and one of three breeds of puppy. This creates an Advanced Linear setup:

PT32-Oct 2000 LGE-G4_srd1.png

The first rule places G on day 1, and the second rule eliminates G from day 2. Thus, day 2 must be N or R. The third rule eliminates G from day 7, leaving day 7 as N or R:

PT32-Oct 2000 LGE-G4_srd2.png

The second rule is represented above as a BB not-block, which indicates that no breed can be featured on consecutive days. This is a more concise representation than drawing all six not-blocks. The third rule is represented with a double-not arrow between 1 and 7.

The fourth rule establishes that exactly three Hs are featured, but that no H is featured on day 1. Thus, M or S must be featured as the kitten on day 1. The fifth rule indicates that R is not featured on day 7. This fact, when combined with the inference that G cannot be featured on day 7, results in the inference that N must be featured on day 7. If day 7 must be N, then from the second rule day 6 cannot be N, and must therefore be G or R.

The fifth rule also establishes that R cannot be featured on the same day as H, which results in a vertical not-block:

PT32-Oct 2000 LGE-G4_srd3.png

Combining the above information results in the following setup:

PT32-Oct 2000 LGE-G4_srd4.png

While the above setup is the final setup for many students, the interaction of the second and fourth rules restricts the placement of the three Hs to just four possibilities:

PT32-Oct 2000 LGE-G4_srd5.png

These four possibilities can be (but do not have to be) used to Identify the Templates:

PT32-Oct 2000 LGE-G4_srd6.png

The only drawback to showing the four templates is that the process can be somewhat time-consuming, and overall the questions can still be done without the templates, albeit less efficiently.

[bknorth]

Hi! I just did the October 2000 game for questions 19-24 (game 16 in the LG Training Type II book) about breeds of kittens and puppies. In setting up the game, does each breed need to be represented? And with the Himalayan kittens, I understand that they can be featured on days 2, 4, and 6; 2, 4, and 7; or 3,5, and 7. Day 7 features the Newfoundland puppy, so Day 6 features either Greyhound or Rottweiler. Is there a further inference I should have made? This game took longer than I wanted.

Thank you!

[Emily Haney-Caron]

Hi bknorth,

Good question. This is a really great game to use templates; you'll end up with 4 possibilities, based on the possible placements of H; H can go on:
2-4-6
2-4-7
2-5-7 or
3-5-7

You'll then want to add in Rules 2 through 4 (and the inferences you identified) to each of those templates. For a game like this, the templates should make it much faster in the end, even though it takes a bit more time up front.

I hope that helps!

[bknorth]

Thank you very much Emily! I appreciate it.

[kristinaroz93]

This game is about three breeds of kitten: Himalayan, Manx, Siamese and three breeds of puppies: Grehound, Newfoundland, Rottweiler.

I wanted to clear something up about this game. Just based on the first 4-5 lines of rules (which are the more general rules before we get to the specific ones) we would not be able to infer that every breed of kitten or puppy has to go right? (as in it doesn't state that every one has to make an appearance in the game). The only reason we eventually know everyone has to go is based on the layout of the actual rules and their implications, but not from those first few lines is what I am trying to figure out. Is this correct?

Also, I had not initially looked and thought this was a double stack game with cats and breeds, I initially thought they were all going in one line with one empty slot. Is what should have given that away immediately was the fact that it said in the rules that R and H do not go on the same day as well as the format of answer choices in question 19.

Thanks in advance!

[Emily Haney-Caron]

Hi Kristina,

Because no breed can be featured on two consecutive days, we know that at least two breeds of each must be included. The next rule, that any breed featured on day 1 cannot be on day 7, allows us to infer that all three breeds will always be included for each animal - with only 2, the same breed would either have to be on days 1 and 7 or on consecutive days.

I'm not sure what you're asking with the second part of your question; could you explain what you mean a bit more?

[KG!]

Is anyone able to do the full setup for the game, like how It is typically done within this forum. I am having trouble with the setup and can't move forward with the questions.

Any help is much appreciated.

[Adam Tyson]

I'm not so great at drawing these in this forum, KG, but I'll describe it.

To start with, this is an Advanced Linear Game, with a base of 7 spaces numbered 1 through 7, and two rows, one for Kittens and one for Puppies. Each day has exactly one of each. Note that the rules never said that all the breeds have to be used! It may be possible to solve this game with no R, for example, or no M.

Next, diagram the rules and plug things into your base. Put a G in the first spot for Puppies, and then not-laws for G under spaces 2 and 7 per the next two rules. Also, draw something to remind you of those two rules, like an XX not-block for the "no consecutive breed" rule and maybe a conditional rule of 1 7.

A not-law for H under 1 is next, and maybe "H=3" or "HHH" in your rule set to indicate 3 Hs.

For the last rule, place an R not-law under 7 and also draw an HR not block (vertically, since they are in different rows).

Now check for inferences, and you should notice that two of the three puppy breeds cannot be 7th, G and R. That means the 7th puppy must be N, so fill that in, and add a not-law for N under space 6.

From there you could set up 4 templates based on the possible placement of the 3 Hs, as described earlier in this thread, or you could charge ahead into the questions and see how that goes.

I hope that helps! Sorry, I wish I was better at creating those pictures!