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#26185
Setup and Rule Diagram Explanation

This is a Linear/Grouping Combination game.

The game scenario asks us to determine the annual bonuses for seven employees. Each employee receives a bonus in the amount of $1k, $3k, or $5k, and each belongs to one of two departments—Finance and Graphics:
June15_game_1_diagram_1.png
Since the bonus amounts have an inherent sense of order, it is best to use them as our base. This creates a Linear/Grouping setup, in which each of seven variables is being assigned to one of three groups. Because each employee must receive exactly one bonus, the game is Balanced. However, since the number of employees receiving each bonus amount is left unclear, the game is Defined-Moving.

Logically speaking, either variable set—the employees or the bonus amounts—can be used as the grouping base. In fact, the answers to the List question use the employees as the base. So, is this a good enough reason to revise your setup? Probably not. Since the bonuses have an inherent sense of order but the employees do not, it would be far easier to represent the implications of the rules if the order were inherent to your base, not to your variable set. Using the employees as your choice of base is not necessarily a mistake, but it is probably less efficient in the long run.

With the basic structure in place, let us now turn to the rules.

The first rule establishes that no one in the Graphics department receives a $1k bonus. This rule creates three Not Laws:
June15_game_1_diagram_2.png
In a highly unusual gesture, the second rule introduces an entirely new conceptual element into the game: apparently, some employees are rated Highly Effective and others are not, which affects the bonuses they can (and cannot) receive. Rules like these are precisely why we urge you to read the entire rule set before diagramming your game. Otherwise, rules like these can easily catch you off-guard.

According to the second rule, any employee who is rated Highly Effective receives a higher bonus than anyone in his or her department who is not rated Highly Effective. Note that the rule does not allow us to compare the bonuses of employees from different departments: it is specifically limited to those working in the same department:
June15_game_1_diagram_3.png
The last rule states that only L, M, and X are rated as Highly Effective. We can use the “HE” subscript to represent this information, or simply circle each HE variable, as shown below:
June15_game_1_diagram_4.png
You should immediately tie the second and third rules together. Since only L and M are rated Highly Effective in Finance, their bonuses must be higher than those of K and P:
June15_game_1_diagram_5.png
Clearly, then, neither L nor M can receive a $1k bonus. Likewise, neither K nor P can receive a $5k bonus. This generates four additional Not Laws:
June15_game_1_diagram_6.png
By the same logic, since only X is rated Highly Effective in Graphics, his bonus must be higher than the bonuses received by V and Z:
June15_game_1_diagram_7.png
Consequently, neither V nor Z can receive a $5k bonus. But, thanks to the first rule, neither of them can receive a $1k bonus either. It follows that V and Z must receive $3k bonuses, whereas X must receive a $5k bonus:
June15_game_1_diagram_8.png
Is it worth representing the Fixed Numerical Distributions that govern the assignment of employees to bonuses? Well, the game does not explicitly mandate a minimum number of employees per bonus, and the rules are not restrictive enough to establish such a minimum for the $1k group. If something seems too laborious, it probably is: a detailed analysis of each distribution is neither required nor encouraged. A far simpler—and probably more useful—task would be to determine the minimum and the maximum number of employees who can receive each bonus:
  • $1k: As discussed earlier, five of the seven employees cannot receive $1k bonuses. In fact, there is no reason why anyone would receive a $1k bonus. Thus, the range of variables in the $1k group is 0-2.

    $3k: Since V and Z must receive $3k bonuses, the minimum number of variables in this group is two. What about the maximum? There are only four remaining employees, two of whom (K and P) must receive different bonuses than the other two (L and M). Clearly, then, at most two additional employees can receive $3k bonuses, bringing the maximum number of variables in this group to four.

    $5k: Since X must receive a $5k bonus, the minimum number of variables in this group is one. Four of the remaining employees (K, P, V, Z) cannot receive the highest bonus, suggesting that the maximum number of variables in this group is three.
Thus, we arrive at the final setup for this game:
June15_game_1_diagram_9.png
 Cbarcelo
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#61881
Hi there,

I set up this game quite differently --- it sets up the solutions and took me about 2 minutes in total to set up and write out the rules. Did I just get lucky or is it something I can continue to work with given I did not pick the same bases but did get all the questions right and was done with the game in 4 minutes.

My set up:

1.
Bonus: 1 3/5 3/5 1 3 5 3
Rating: E E E
Department: F F F F G G G
K L M P V X Z

2.
Bonus: 3 5 5 3 3 5 3
Rating: E E E
Department: F F F F G G G
K L M P V X Z

PS. I apologize for the spacing. It seems the system formats it once I submit =(
 LetsGetThis180
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#61899
My setup looks exactly like this although I have one question about an inference that wasn't really specified above. If V, X, Z, L, and M can't receive $1,000 can it be okay to infer that K or P (or both) could be the only ones that could receive $1,000? I don't think placing a dual option would be a safe bet since it could also mean there could be no one receiving $1,000. Is there any other way I could write this down or should I just make a mental note? Thanks!
 James Finch
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#62073
Hi LetsGetThis,

This is something that will come down to individual choice, as there isn't a quick and easy way to note all the possibilities with visual shorthand. As you note, you can safely eliminate 5 of 7 options for the 1K group, leaving only K or P, including the possibility of both or neither. As I would have gotten to that inference by using Not Laws (writing those that are excluded from the group above the group's name), I personally would have left those in place and simply made a mental note and moved on. However, I could also imagine writing something like "Only K or P possible" under the group's column, especially if I was worried I may not remember the specific inference.

Hope this helps!
 Kamm170
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  • Joined: Oct 11, 2020
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#79947
Hi! How do you know when it is best to determine the minimum and the maximum numbers for each group in a grouping game? I worry that I may spend time doing this and it may be irrelevant when it comes to the questions. :-?
 Jeremy Press
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#79973
Hi Kamm,

In Partially Defined and Undefined grouping games, it's always a good idea (before you dive in on questions) to think at least briefly about minimums and maximums. So basically, if there's a grouping component to the game, and I cannot tell from the information given in the scenario what the min and max are for the group (or groups), I'll always think at least briefly about that issue. How much time do I spend on it? Not too much (30 seconds? a minute?). I just want to pay attention to the fact that it's a point of uncertainty, and try to help myself narrow that uncertainty as much as I can under the time constraints.

One additional observation: it's a little harder in this game than in many games to determine all the minimums and maximums. But that's not a good reason to ignore the issue. The designers of the game know this is a harder/more time consuming issue to get clear on. They reward you for doing it on multiple questions in the game!

I hope this helps!

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