Any of the following could be true EXCEPT:

mjenei on July 1, 2019

Explanation

Could this game be drawn out and/or explained?

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Emil-Kunkin on April 28 at 02:40PM

This is a linear game that requires us to determine the order of visits to four out of six cities - H J M O S T. Each city is visited only once. We have the following rules:

(1) H and T must be included in the tour but they cannot be visited consequently.

This rule tells us that H and T must appear on our schedule, and both appear exactly once but not next to each other, there must be at least one or two other cities between them.

___ ___ ___ ___ H T

(2) if O is included in the tour, S cannot be.
Conversely, we can infer that if S is included in the tour then O is not. These two visits are mutually exclusive, meaning only one of them could be visited or neither, which leaves us with two possible scenarios for a complete list of visited cities:

H T S/O J/M
H T J M

O -> ~S
S -> ~O

(3) If J is visited, it must be third.

J -> 3d

(4) If both J & M are included they must be visited consecutively.
We can see that the only way both J and M could be included is if both S & O are excluded, meaning the complete list of cities visited in that scenario is:

H T J M

Since JM must be consecutive and H T cannot be consecutive, we can infer that H and T must be in positions 1 or 4 and MJ in positions 2 and 3 respectively (remember J must always be 3d)

H/T M J H/T

Putting all the rules together we have the following setup

(1) H/T M J H/T
(2) ___ ___ __ __ H T S/O M/J

~HT (not consecutive)
J = 3d

For this question, b is correct because If j is in it must be third, so we would have _ _ J M, which would violate the rule that h and t can't be next to each other.