If Kwon is assigned to be leader for exactly one of the committees, then for which of the committees is the assignmen...

Skylar on June 23, 2020

@saskipper, happy to help!

Our deductions during setup allow us to come up with two possible scenarios for this game:

(#1)
X: N (H/K) (K/H)
Y: K J H
Z: N (H/M) (M/H)
L S T

(#2)
X: N (H/K) (K/H)
Y: (H/N) J K
Z: N (H/M) (M/H)
L S T

With this setup in mind, we look to your specific question. We are told that K is assigned to be the leader for exactly one of the committees. In our above scenarios, N is always assigned as the leader in committees X and Z. This means that the only committee K can be the leader of is Y. This is the case in our first scenario above, wherein Y is the only committee with fully determined placements. Therefore, (B) is correct.

If you didn't get this GURU setup, don't panic. Let's walk through how to solve this problem if we weren't able to make all of the deductions above.

We are told that K is the leader for exactly one of the committees. Rule #3 says that K cannot be assigned to committee Z, so this only leaves X and Y as options. If we assign K as the leader of X, we will run out of variables to fill the committees. This creates an invalid scenario, meaning that K cannot be the leader of X. No worries, let's try making K the leader of Y instead. Remember, Rule #4 tells us that J is the secretary of Y. This gives us:
X: __ __ __
Y: K J __
Z: __ __ __
L S T
Looking at the numbers (i.e. 5 volunteers with various limitations, 9 spots, 3 volunteers per committee), we can determine that J and M appear once, K appears twice, and H and N appear either twice or three times. This is a key deduction. Now, note that Rules #3 and #4 say that neither K nor J can be assigned to Z. This means that the three remaining variables - N, H, and M - must all be assigned to Z. Rule #1 says that if N is used, it is the leader. So, N is the leader of Z. We do not know which role H and M play in Z. Yet, we know that N must be used two or three times, and since K is one of the leaders in this question, we can deduce that N is used exactly twice. So, N is the leader of X. Also, we know that K is used twice and Rule #3 says that K is not in Z. This means that K must be used in X. H is the only variable left that can fill the remaining spots, which gives us:
X: N (H/K) (K/H)
Y: K J H
Z: N (H/M) (M/H)
L S T
As we can see, Y is the only fully determined committee, so (B) is correct.

Does that make sense? Hope it helps! Please let us know if you have any other questions!