Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

Here is the full setup as produced by the game scenario and rules. A discussion follows thereafter.

PT39-Dec2002_LGE-G3_srd1.png

Because there are seven years and only five children, this linear game is Unbalanced. However, this imbalance is easily corrected by creating two empty years, designated by the “E’s” above. Since an E in either the L/R row or the child row means that the entire year is empty, we can show the two empty years as:

PT39-Dec2002_LGE-G3_srd2.png

This game requires a series of related steps to create the complete setup above:

Step 1. The combination of the first rule and the fifth rule allows us to infer that a left-handed child was not born in 1990 or 1992.

Step 2. U, a right-handed child, was born in 1993. Thus, a right-handed child was not born in 1992 or 1994. Further, from the third rule we can infer that S, a left-handed child, was born in 1990, 1991, or 1992. However, when this inference is combined with step 1, we can infer that S was born in 1991.

Step 3. Since neither a left-handed nor a right-handed child can be born in 1992, 1992 must be an empty year. Since a left-handed child cannot be born in 1990, 1990 must be either an empty or a right-handed year.

Step 4. From the first three steps above, we have placed one right-handed child, one left-handed child, and one empty year. Further, 1990 has been established as either an empty or a right-handed year.

Consequently, two left-handed children must be born in the years 1994, 1995, and 1996. Because of the first rule, we can therefore infer that the two left-handed children are born in 1994 and 1996. From that inference we can deduce that 1995 is the remainder of the right-handed/empty dual-option from 1990. At this point, the entire L/R row is complete, and the only uncertainty is in 1990 and 1995.

Step 5. Due to steps 1 though 4 above, all the rules are “dead” except the fourth rule. The fourth rule is the only remaining active rule, and even then there are limitations, as shown by the dual- and triple-options in the child row of the diagram.

The discussion above reveals the deep restrictions in this game. In fact, there are only two basic templates that exist:

PT39-Dec2002_LGE-G3_srd3.png

Either the original diagram or these two templates can be used to effectively attack this game.

[glasann]

Hello!

Are you able to post what the set-up for this game should look like? It's really helpful to check my set-up against what you have.

Here's what I have: double baseline, with one slot for L or R and the other for each student. Not blocks for LL and RR, S(L)—RU(R), and Z before T and W

Inferences:
S(L) has to go in 91
U(R) has to go in 93
92 is blank
Z has to go in 90 and is L-handed. At first I thought it could go in 90 OR 94 but I think actually that 90 and 96 have to be filled
T and W have to go in 4,5, or 6 (put in hurdle the uncertainty cues) there but one HAS to be in 6 so either 4 or 5 is blank
1990 is either blank or has Z and, if its in 1990, Z would be right-handed.

Thank you!

[Adam Tyson]

I am not great at creating images in this forum, rademaker1, but I can tell you that most of what you described is correct. However, you have said two conflicting things about Z, and only one of them is correct:

Z has to go in 90 and is L-handed...1990 is either blank or has Z and, if its in 1990, Z would be right-handed.

Z can go in 1990, in which case Z would have to be right-handed, but Z can also go in 1994, in which case Z would have to be left-handed, because 1994 and 1996 must both have left-handed children. That is the only way to get three left-handed children who are not born in consecutive years.

Also, this, which is related to the above point:

one HAS to be in 6 so either 4 or 5 is blank

1994 cannot be a blank space - there must be a left-handed child born in that year.

So, either Z is in 1990 and is right-handed, with T and W in 1994 and 1996 (either order), and they are both left-handed, or else Z is in 1994 and is left-handed, with T and W in 1995 and 1996 (in either order), with the 1995 child being right-handed and the 1996 child being left-handed. That might even be worth setting up two templates based around the placement of Z!