# Which one of the following is a permissible assignment of rangers to park areas?

suzanne on October 24, 2019

Game setup

May we have a set up for this game please?

Replies

Irina on October 25, 2019

@suzanne,

The game requires us to assign each of the six rangers - J K L M O P - to 3 areas -1 2 3. This tells us that every ranger must be assigned to one of the areas, we cannot leave anyone out. Each area must have at least 1 and at most 3 rangers. This tells us that there are two possible combinations of the number of rangers per area:

3-2-1
2-2-2

The following rules apply:
(1) M is assigned to 3.

3: M

(2) Neither O nor P are assigned to area 1.
Combined with rule (1), we can infer that J/K/L are the only possible assignments for area 1.

1: J/K/L

(3) L is assigned to the same area as K or M but not both.

This rule tells us that we must have either LK or LM combination but not LKM in the same area, meaning K cannot be assigned to area 3.
Note that if L is assigned to area 1 or 2, it must be paired with K, and if it is assigned to area 3, it must be paired with M
1: LK
2: LK
3: LM

We can also infer that if L is assigned to area 2, it must be paired with K and the only ranger that is assigned to area 1 in this scenario is J:
1: J
2: LK
3: M

(4) if O is assigned to 2, then JK are assigned to the same area, otherwise they are assigned to different areas.
O-2 <-> JK
~O-2<-> ~JK

Combined with the previous rule, we can infer that if L is assigned to area 2, O must be assigned to area 3, and P could be assigned to either 2 or 3:

1: J
2: LK /P
3: MO /P

Now let's consider the impact of O assignment to area 2 or 3:
If O is assigned to area 2, L must be assigned to either area 1 or 3:

1: J K L
2: O /P
3: M /P

or
1: J K
2: O /P
3: M L /P

If O is assigned to area 3, L could be assigned to area 3 along with M and O, area 2 with K or area 1 with K.

P is the only free variable in these scenarios and could be assigned to either area 2 or 3 interchangeably.

Taken together, we have the following rules:
1: J/K/L
2:
3: M ~K

LK v LM
O-2-> JK -1
O-3 -> ~JK
L-2:
1: J
2: LK /P
3: MO /P

The question asks which of the following could be a permissible assignment.
(A) Incorrect. L must be paired with M or K.
(B) Incorrect. If O is in area 2, KJ must both be in area 1.
(C) Incorrect. P cannot be assigned to area 1
(D) Incorrect. M must be assigned to area 3
(E) Correct. This assignment complies with all the rules.

Let me know if this makes sense and if you have any further questions.

melissahamilton316 on September 10, 2020

is this a group game?