Which one of the following could be the assignment of managers to cities?

on October 19 at 01:10AM

Setup

Could we please have a setup for this game? Thanks

1 Reply

Irina on October 19 at 01:33AM

@suzanne,

The game involves four product managers - F, G, H, and I sent to visit three cities - M, S and T. Each manager will visit at least one of the cities, and each city will be visited by exactly two managers, meaning there are six visits total.

___ ___ ___
___ ___ ___

M S T

The following rules apply:

(1) I must visit exactly 2 of the cities.

This rule tells us that there are 4 visits left to be assigned to the remaining 3 managers meaning none of the managers could visit all 3 cities, but one of the remaining managers must visit 2 cities, and two managers must visit one city each. 2 (I) -2 -1 -1 is the overall distribution of visits.

(2) F & H cannot visit the same city as each other.

~FH

(3) If M is visited by G, then T must be visited by H

M (G) -> T(H)

(4) G cannot visit Sydney

S (~G)

___ I ___
___ F/H ___

M S T
~G

This rule tells us that we must pick 2 managers from F H I to visit Sydney. Since F & H cannot visit the same city per rule (2), we must pick I to visit Sydney and either F/H.

The question asks which of the following could be an assignment of managers to cites:

(A) is incorrect because I must visit 2 cities
(B) is incorrect because I must visit S.
(C) is correct and complies with all the rules.
(D) is incorrect because if G visits M, H must visit T
(E) is incorrect because F & H cannot visit the same city.

Let me know if you have any further questions.