# Which one of the following must be true?

on March 14 at 03:12AM

Irina on March 14 at 05:14AM

@ChristianJM,

The answer to "must be true" questions is most often found in the initial setup. The game requires us to determine the schedule of 5 students - G H J K L who work exactly two shifts for a total of ten shifts over five days.

1 ___ ___ ___ ___ ___ G __ G H or J
2 ___ ___ ___ ___ ___ LL J H
M T W Th F
K K
The rules tell us that:

(1) No student works both shifts of any day, so we must have two different students each day.
(2) L works the second shift on two consecutive days.

This rule tells us we must have LL combination somewhere in our schedule for the second shift.

(3) On two nonconsecutive days, G works the first shift.

(4) K works on T & F.

(6) H & J work on the same day as each other at least once.

H
J

(6) G & L never work on the same day as each other.

This is a restrictive rule, let's think about possible combinations,

G K ___ H G
__ L L J K

__ K G H G
L L __ J K

H G __ __ G
J K L L K

Note that H & J shifts are interchangeable for each of these scenarios.

Now let's look at the answer choices:

(A) G does not work on T.
Incorrect, scenario 3 allows G to work on T.

(B) H does not work on W.

Incorrect because there are no restrictions on when H's second shift must be. One of his shifts must be with J but his second shift is a free variable and could be on any open day.

(C) J does not work on T.

Correct. In all three scenarios, K & L or G & K must work on T.

(D) J does not work on Th.

Incorrect. Scenario (1) allows J to work on Th.

(E) L does not work on T.

Incorrect. Scenario 2 allows L to work on T.

Let me know if you have any other questions.