**Note: **If you’re coming to this explanation from a later question, see the note at the bottom of the page. This game is unusual in that the diagrams discussed in this question solve *every *question.

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This question asks what must be true. So if you can find a *single *scenario where an answer isn’t true, then that answer is wrong.

The first question is useful. If you drew in the other half of the correct answer, you have a full, valid scenario. I’ve drawn it here, noting which variables are interchangeable:

H and J in Monday/Wednesday are interchangeable. And likewise, H and J are interchangeable between the first and second shifts on Thursday. We’ll be using this diagram on later questions.

It’s *extremely *important to know which variables are interchangeable. The fact that H and J are largely interchangeable makes this game very easy.

On this question, the above diagram eliminates **D **and** E. **Joe can work Thursday, and Louise can work on Tuesday.

After eliminating those two answers, I didn’t know where to start. So I just decided to make a scenario where **A **was true. If it worked, I’d disprove **A,** and the scenario might disprove other answers too.

So I placed Grecia Tuesday and Friday. This was to leave space for Louise to go twice in between (rules 2, 3 and 6):

Next, we have to put Katya on Tuesday and Friday (rule 4) and Hakeem and Joe together on one day (rule 5):

Note that there was only *one *way to place Katya and H/J. However, H and J are reversible Monday because it doesn’t matter who has the first shift.

Finally, one more H and J are left to place. These go in the only space left, and they’re interchangeable:

It’s important to note who is interchangeable: H and J, where joined by curves. Knowing what can be changed will let you use this diagram on other questions.

Also note that I’ve used curved lines, rather than the traditional H/J, J/H. The lines make for a simpler diagram which is easier to read. If your diagram is cluttered, your thinking is cluttered.

This diagram eliminates **A **and **B. **It’s possible for Grecia to work Tuesday, and for Hakeem to work Wednesday.

**C **is **CORRECT. **

On review, it’s worth thinking about why **C **doesn’t work. If you try drawing Joe Tuesday, you’ll see why. First, Katia must also go Tuesday:

Next, we have to place Louise and Grecia somewhere. Anywhere is fine as long as you obey rules 2, 3 and 6:

And now we see the problem. There’s no way to put Hakeem and Joe on the same day (rule 5).

**If you’re coming from a later question**

This game is unusual in that the two diagrams I discussed in this question solve *every *question. So I’ll be referring back to this question frequently on later questions. If you are at all confused about how to draw the diagrams, do them again now, as you’ll need them on later questions.

Here are the two diagrams. The first is the right answer from question 14, the second was drawn for this question.

On both diagrams I’ve indicated where H and J can change positions, with boxes in the first diagram, and with lines in the first and second.

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