The assignment of volunteers to days is completely determined if which one of the following is true?

Filippo on August 20 at 02:34PM

Why is C correct

Could anyone please show why C is correct? How does placing M (and thus L) on Friday complete the assignment of all places? Thank you very much!

4 Replies

Shunhe on August 21 at 01:42AM

Hi @filozinni,

Thanks for the question! So we’re trying to completely figure out the assignment of volunteers to days here. Well, let’s put M on Friday and see what happens!

So we put M on Friday. Well, that means L works on Friday. And we already know from rule 3 that N works on Friday. So Friday is set, since it’s LMN.

Now let’s think about Saturday. What do we know about Saturday? It’s not a rule, but we know that L has to work on Saturday. Why? Because we know that P doesn’t work on Saturday, which means 3 out of 4 of LMNQ work on Saturday. Is it possible to not pick L? Well, if we don’t pick L, that means we pick MNQ. But if we pick M, we have to pick L! So it’s impossible to not pick L, so L always goes on Saturday. So L is on Saturday and Friday, which means from rule 1 that L can’t work on Thursday.

OK, now pause, let’s think about Thursday. If L can’t work on Thursday, that means M can’t work on Thursday (by the contrapositive of the second rule). But that means three people are left for Thursday: NPQ. So Thursday is set now too.

Now back to Saturday: if N is on Thursday and Friday, then N can’t be on Saturday (from rule 1). And again, we know that P doesn’t work on Saturday. So now we’re down to three again: LMQ. And that decides Saturday, which means we’re good on all days! So putting M on Friday determines everyone.

Hope this helps! Feel free to ask any other questions that you might have.

Filippo on August 21 at 08:07AM

This explanation helped me a lot! I had not made the - quite big - deduction that L is always on Saturday, and that's why I was so confused. Thanks as always for the great explanation, @Shunhe!

Shunhe on August 21 at 07:18PM

You're welcome! That's a pretty important one for this game and helps a lot, but it's hard to catch at first.

on September 11 at 05:47AM

Any advice on learning how to make deductions like this? I keep practicing but can't seem to ever make these crucial deductions that save enough time to finish the section.