Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Moving, Balanced, Numerical Distribution game.

In this game, five employees each hold one of three positions. The twist comes in that two of the employee levels—manager and technician—are supervised. Let’s examine the numerical spread of the positions first.

The first rule establishes that there is exactly one president. The next two rules establishes that there is at least one manager and at least one technician. Thus, all three positions must be filled by the five employees, which establishes a minimum of a 1-1-1 spread for the distribution:

PT14-Feb 1995 LGE-G1_srd1.png

Thus, two employees remain to be distributed. Because there is only one president, those two employees must be distributed between the managers and technicians. This leaves three possibilities:

PT14-Feb 1995 LGE-G1_srd2.png

However, take a closer look at the statement in the scenario that “employees are supervised by exactly one employee.” For this to be true, the 1-3-1 distribution cannot occur because the three managers would all have to supervise the same technician. Thus, there can be only two distributions in this game:

PT14-Feb 1995 LGE-G1_srd3.png

From a supervisory standpoint, these are the rules for each employee:

President:      Is not supervised. Must supervise one or two managers; can supervise technicians as well in the 1-1-3 distribution.

Manager(s):      Is/are supervised by the president. Must supervise one or more technicians.

Technicians:      Are supervised by president or manager. Do not supervise anyone.

Let’s now combine the distributions with the supervision possibilities, with the last two rules as well:

PT14-Feb 1995 LGE-G1_srd5.png

In the distributions above, the arrows indicate supervision assignments.

H, K, and L are all randoms, so your focus must be on F and G as you assess the game. Because F does not supervise any employee, F must always be a technician. Consequently, G is the only employee who has any restrictions, and these restrictions can be applied to the two distributions:

In the 1-2-2 fixed distribution, G cannot be a manager because each manager supervises only one employee, and the last rule indicates that G must supervise exactly two employees. Hence, in the 1-2-2 fixed distribution G must be the president.

In the 1-1-3 fixed distribution, G could be either the president or a manager. Because of the last rule, however, the supervision assignments are fixed: if G is the president, the G must supervise the manager and one technician, and if G is the manager, then G must supervise two technicians. Therefore, regardless of G’s assignment, in the 1-1-3 fixed distribution the president always supervises exactly two employees and the manager always supervises two employees.

With the information above, we are ready to attack the questions.

[esp165]

Even after reading the Encyclopedia, I still do not understand why were are limited to two set ups. To be specific, why in the 1-1-3, could the President not supervise the one manager and two of the three technicians?

[Dave Killoran]

Hey ESP,

Without considering any of the rules about the specific variables, initially it appears that the scenario you propose could occur. But, once you consider the restrictions on certain variables, it becomes impossible. Let's look at why.

We know that G cannot be a Technician, so G is always a Manager or President. The last rule indicates that G supervises exactly two employees. In the scenario you propose, the Manager supervises one employee, and the President supervises three employees. That's a big problem for G, because that means G can't be the Manager or President. And since G can't be a Technician either, ultimately we are left in a situation where we cannot create a viable solution.

Please let me know if that helps explain what is going on. Thanks!

[esp165]

Missed that piece of the puzzle. Thank you.

[szamias]

Hi, I am trying to figure out how to do this game? I have been unable to lock down the drawing I should be doing and I was also unable to lock down any not laws as the rules are too abstract.

Does anyone know how to set this game up?? If so, can someone please help me!??

[Dave Killoran]

Hey Szamias,

Let me try to help you out here. There are a couple of things to recognize in this game:

First, there can be only two distributions in this game:

P - M - T

1 - 2 - 2 = 5

1 - 1 - 3 = 5

Second, once you have the distributions, make sure to consider who can manage who (because it is different in each distribution).

Third, H, K, and L are all randoms, so your focus must be on F and G as you assess the game. Because F does not supervise any employee, F must always be a technician. Consequently, G is the only employee who has any restrictions, and these restrictions can be applied to the two distributions (see the next point).

Finally, consider some of the assignment possibilities in each distribution: In the 1-2-2 fixed distribution, G cannot be a manager because each manager supervises only one employee, and the last rule indicates that G must supervise exactly two employees. Hence, in the 1-2-2 fixed distribution G must be the president.

In the 1-1-3 fixed distribution, G could be either the president or a manager. Because of the last rule, however, the supervision assignments are fixed: if G is the president, the G must supervise the manager and one technician, and if G is the manager, then G must supervise two technicians. Therefore, regardless of G’s assignment, in the 1-1-3 fixed distribution the president always supervises exactly two employees and the manager always supervises two employees.


That should get you started, but please feel free to let me know if you run into any specific problems. It's a bit of an unusual game at first glance (the supervisory aspect in particular), but once you get past the initial uncertainty, it is pretty straightforward (and exactly the type of thing that could appear on any given test).

Good luck!

[szamias]

Thank you!! That was very helpful. If only you were there with me on exam day. HAHA! Hopefully I can see the more wordy games as clearly now thanks to your help.

[Checkmate]

Hey Dave,

According to rule #3 Each manager supervises at least one employee. So how did you make the inference that "each manager only supervises one employee." I am having a hard time understanding that. I do understand the 1-2-2 and 1-1-3 ratios. .

Hey Szamias,

Let me try to help you out here. There are a couple of things to recognize in this game:

First, there can be only two distributions in this game:

P - M - T

1 - 2 - 2 = 5

1 - 1 - 3 = 5

Second, once you have the distributions, make sure to consider who can manage who (because it is different in each distribution).

Third, H, K, and L are all randoms, so your focus must be on F and G as you assess the game. Because F does not supervise any employee, F must always be a technician. Consequently, G is the only employee who has any restrictions, and these restrictions can be applied to the two distributions (see the next point).

Finally, consider some of the assignment possibilities in each distribution: In the 1-2-2 fixed distribution, G cannot be a manager because each manager supervises only one employee, and the last rule indicates that G must supervise exactly two employees. Hence, in the 1-2-2 fixed distribution G must be the president.

In the 1-1-3 fixed distribution, G could be either the president or a manager. Because of the last rule, however, the supervision assignments are fixed: if G is the president, the G must supervise the manager and one technician, and if G is the manager, then G must supervise two technicians. Therefore, regardless of G’s assignment, in the 1-1-3 fixed distribution the president always supervises exactly two employees and the manager always supervises two employees.


That should get you started, but please feel free to let me know if you run into any specific problems. It's a bit of an unusual game at first glance (the supervisory aspect in particular), but once you get past the initial uncertainty, it is pretty straightforward (and exactly the type of thing that could appear on any given test).

Good luck!

[Dave Killoran]

Hi Checkmate,

I made that comment in reference to the 1-2-2 distribution only, where there are two managers, and from the third rule each must supervise at least one employee. But, since there are only two employees, each manager can supervise only one of the two employees. Thus, G cannot be a manager in that scenario, and must be president.

Please let me know if that helps. Thanks!

[atirvine88]

Hey guys,

This problem also gave me some trouble. I found myself having to keep going back to the rules to reread to make sure I was making correct references. Is there a way to efficiently and accurately represent the rules and/or inferences- or are these things I should just try to keep in mind going through the game?