- Tue Apr 20, 2021 11:57 am
Below is a basic write-up of the structure, rules, and inferences in the game, as well as a basic diagram of the same. Hopefully this helps!
1. The scenario makes clear that at least part of the task in the game is a grouping task. We must assign each of 6 letters to exactly one of 3 spoonfuls. This creates a Defined grouping scenario, in which we know that the total number of grouped variables (across the 3 spoonfuls) will equal 6.
2. The scenario does not fully define how many variables will appear in each spoonful, instead giving us a minimum (1) and maximum (3) for each spoonful. This creates a Distribution uncertainty in the game, and it is to our benefit to determine the distributional possibilities in advance. With 6 variables, and a minimum of 1 in each spoonful, there are two distributional possibilities: 2-2-2, and 3-2-1. The distribution is unfixed, because in the 3-2-1 distribution, we do not have sufficient information to determine which spoonful gets 3, which gets 2, and which gets 1 of the letters.
3. The rules clarify that there is also a sequencing component to the game, using language about which letters are "later" than other letters. These rules require us to use sequencing diagrams, and to pay attention to Not Laws.
4. The first rule places U in a later spoonful than T. This allows us to infer that T is not in the 3rd spoonful, and U is not in the 1st spoonful (see the Not Laws in the diagram).
5. The second rule is phrased negatively. Since U is not in a later spoonful than X, U is either before X, or U is in the same spoonful as X. This is represented diagrammatically using the "Double Dash" diagram. Since X will not be able to come before U in the diagram, this means we can add a Not Law for X underneath the 1st spoonful.
6. The third rules places Y in a later spoonful than W. This allows us to infer that W is not in the 3rd spoonful, and Y is not in the first spoonful. There are now only three possibilities for the 1st spoonful: T, W, and Z.
7. The fourth rule places U in the same spoonful as either Y or Z, but not both. Block diagramming represents this rule. Since it is uncertain which of Y or Z is with U, there are no additional Not Law inferences we can draw for Y or Z. The "not both" component of this rule is difficult to represent diagrammatically, so it would be advisable to highlight or underline this part of the rule so that it is not forgotten.
8. The diagram below depicts the rules, inferences, and a Template for the 2-2-2 distribution. The 3-2-1 distribution is far too open-ended to permit an efficient use of templates, so it is not advisable to pursue templates using that distribution.