If Morse works on Thursday, which one of the following must be true?

MrLaw on February 9, 2020


I've done 21 permutations of this and I cannot achieve a scenario where either Q DOESN'T work Friday or Morse DOESN'T work Saturday...

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MrLaw on February 9, 2020

Annndddddd I figured it out on permutation 22... Nevermind. I see what information I needed. Still, I feel like it took me forever to work out.

Irina on February 12, 2020


The quickest way to approach this question is to refer to the initial setup instead of trying different scenarios. We have 5 volunteers L M N P Q and 9 open slots to fill. No volunteer can work on all three days, which means we have 4 volunteers working 2 days and 1 working 1 day:

Since M & L always go together, L must definitely volunteer 2 days though M could volunteer one.

This specific question asks if M works on Th, which of the following must be true. Well, we know that if M works on Th, then L works on Th as well. Where can the second L go?

Th M L ___
F N ___ ___
S ___ ___ ___ ~P

There are two different options here - M works two days or M works one day. If M works two days, then the only day the second M & L pair could go is Sat.

It cannot go on F because then there is no space left for P & Q:

Th: M L P
F: N M L
S: Q ??

This scenario results in P & Q only volunteering for one day, which is impossible per our inference above. Hence we can conclude that M & L must go on S:

Th: M L P/Q
F: N P Q
S: M L Q /N

The second option is if M only volunteers for one day.

Th: M L P
F: N P Q
S: Q N L

In this scenario, every other volunteer must volunteer for two of the days. Since P cannot volunteer on S, we know that P must go on Th & F. The only remaining spots for Q are F & S. And the remaining volunteers N & L must go on Sat as well.

Just by looking at these two scenarios, we can see that the only condition that must be true is that Q works on Friday.

Let me know if this makes sense or if you have any other questions.