Seven People A, B, C, D, E, F, G plan to enjoy boating.There are only two boats, and the following conditions are to be kept in mind.(I) A will go in the same boat in which E is to go.(II) F cannot go in the same boat in which C is, unless D is also accompanying.(III) Neither B nor C can be given the boat in which G is.(IV) The maximum number of persons in one boat can be four only.If E gets the boat with F, which of the following is the complete and accurate list of the people who must be sitting in the other boat?
Question
Seven People A, B, C, D, E, F, G plan to enjoy boating.There are only two boats, and the following conditions are to be kept in mind.(I) A will go in the same boat in which E is to go.(II) F cannot go in the same boat in which C is, unless D is also accompanying.(III) Neither B nor C can be given the boat in which G is.(IV) The maximum number of persons in one boat can be four only.If E gets the boat with F, which of the following is the complete and accurate list of the people who must be sitting in the other boat?
Solution
The conditions given in the problem are:
(I) A will go in the same boat in which E is to go. (II) F cannot go in the same boat in which C is, unless D is also accompanying. (III) Neither B nor C can be given the boat in which G is. (IV) The maximum number of persons in one boat can be four only.
Given that E and F are in the same boat, and from condition (I), A must also be in the same boat. This leaves us with B, C, D, and G for the other boat.
From condition (II), since F is not in the same boat as C, D does not need to accompany C. Therefore, D can be in either boat.
From condition (III), neither B nor C can be in the same boat as G. Therefore, G must be in the boat with A, E, and F.
This leaves B, C, and D for the other boat. Since the maximum number of persons in one boat can be four only (condition IV), and there are already four people in the boat with A, E, F, and G, B, C, and D must all be in the other boat.
Therefore, the complete and accurate list of the people who must be sitting in the other boat is B, C, and D.
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