Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Balanced, Numerical Distribution, Identify the Templates game.

The game scenario establishes that five witnesses will testify at a hearing held over a three-day period. While the scenario states that each witness testifies on exactly one day of the hearing, it is not clear whether a witness testifies on each day. However, this bit of confusion is cleared up in the rules.

With each day shown on the diagram, the initial setup appears as follows:

PT68_Game_#2_setup_diagram 1.png

Because there are five witnesses testifying over three days, there is a numerical distribution in play. However, we will wait to analyze that element until after each rule has been examined.

The first rule states that F and G do not testify on the same day. Because there is a vertical element in this game, this should be shown as a vertical not-block:

PT68_Game_#2_setup_diagram 2.png

The second rule stipulates that I testifies on Wednesday:

PT68_Game_#2_setup_diagram 3.png

The third rule establishes that exactly two witnesses testify on Tuesday:

PT68_Game_#2_setup_diagram 4.png

The fourth rule eliminates H from testifying on Monday, which can be shown with a Not Law:

PT68_Game_#2_setup_diagram 5.png

The fifth rules establishes that at least one person testifies on Monday, which—because two people testify on Tuesday, and I testifies on Wednesday—means that at least one person testifies on each day. This allows us to fully analyze the numerical distributions in the game.

With 5 witnesses spread over three days, and a minimum of one witness a day, there would normally be two unfixed distributions: 3-1-1 and 2-2-1. But, because the third rule fixes Tuesday with exactly two witnesses, only the 2-2-1 distribution is in play, and because one of the days is set, there are only two possible fixed distributions:

PT68_Game_#2_setup_diagram 6.png

These two distributions limit the game significantly, and suggest that showing the basic templates would be a good attacking strategy. Let’s look at each:

Template #1: The 2-2-1 Distribution
In this distribution, Wednesday is completely occupied by I. F and G must then be split between Monday and Tuesday, which can be shown with an F/G dual-option on each day. H, which cannot testify on Monday per the fourth rule, must testify on Tuesday, leaving J (a random) to testify on Monday:

PT68_Game_#2_setup_diagram 7.png

Template #2: The 1-2-2 Distribution, H testifies on Tuesday
In this distribution, H testifies on Tuesday, leaving exactly one space open on each day. Those three spaces are occupied by F, G, and J:

PT68_Game_#2_setup_diagram 8.png

Template #3: The 1-2-2 Distribution, H testifies on Wednesday
In this distribution, Wednesday is completely occupied by I and H. F and G must then be split between Monday and Tuesday, which can be shown with an F/G dual-option on each day. That leaves only Tuesday available for J to testify:

PT68_Game_#2_setup_diagram 9.png

The three Templates above capture the full range of possibilities in the game, and make the game relatively easy.

[SGD2021]

Hello, in a game situation like this, do we just assume that each witness only goes once each day (so no witness can go twice in each day) because of common sense?

[Adam Tyson]

It doesn't matter if a witness testifies more than once on a given day, SGD2021, because they are still just one person. Going twice wouldn't satisfy the requirement that exactly two people testify on Tuesday, for example, no matter how many times that person testifies. This game isn't about how many times people testify, and there is no element of order on a given day, so it's just about the groups. So it's not so much about common sense but about relevance - it just doesn't matter how many times one person testifies, as long as they only do it on one day!