Confused About Game Solution p 216

• November 16, 2017 at 12:53 pm #3354
vicki
Participant

I am confused at how Mike came to his solution about why spot 3 and 9 must be filled.

Stimulus:
Sarah will host 5 out of town friends- M,N, O, P and Q- at her house over the course of 7 months. The 1st one in March and the last one in September.
She will host each friend once and no more than one friend per month.
During this time period, she will not go 2 consecutive months without hosting an out of town friend.

She will host P after she hosts both M and Q.

She cannot host M in any odd numbered month and she cannot host anyone the month after she hosts M.

N visits in Aug or Sep.

Question: If P visits in July, which of the following must be true?
E. N visits in September.

I also did not understand the conclusion to the 2nd question.
2. If O stays the month after Q but at some point before M, for how many visitors do we know what month they visited?
Ans- C. 3

I understand why M must go in 6 and 7 must be blank. How do I know that QO must go in 3 and 4? Why not 5?
Also how do I know that P goes at the end?

Thanks, sorry, this is confusing for me. Never had a logic class in college and it’s been over 10 years since I graduated.

Any help would be appreciated.

• November 17, 2017 at 4:33 pm #3360
Mike Kim
Keymaster

Hi Vicki —

Nice to have you here and happy to try and help —

If I’m understanding you correctly, I think all of your concerns are related, in that they all stem from 3 and 9 having to be filled. Speaking of — here are the answers to your Q’s —

1) The reason why 3 and 9 must be filled is because it is stated, in the scenario, that the first friend visits in 3 and the last in 9.

2) For question #1, If P is in 7, per the fact that M must go before P and per the third rule, the only place for M to thus go is in 4, and 5 must be left open.

Now we have 3 elements left to place – N, O, and Q.

Per the scenario, 3 and 9 must be filled.

Per the first rule, because 5 can’t have an element 6 now must also be filled.

That means there is no other element to fill 8, and so 8 cannot have an element.

Since N must go in 8 or 9, and 8 cannot have an element, N must go in 9.

3. For #2, if O is right after Q but at some point before M, as you said, M must go in 6 and 7 must be blank.

And we know P must go after M so it will be in 8 or 9, and we know N must also be in 8 or 9.

And the reason the Q O pairing must be in 3 and 4, as opposed to 4 and 5, is because 3 must be filled, and otherwise there would be no other element remaining to fill it.

Hope that clears things up and let me know if you need anything else —

Mike

• November 17, 2017 at 11:42 pm #3361
vicki
Participant

Hi Mike,
Thanks so much for clarifying. I guess I didn’t actually think you meant that someone visits in March and someone visits in September. An oversight on my part.
This explanation helps a lot!
I appreciate it!
Vicki

• November 20, 2017 at 3:20 pm #3371
Mike Kim
Keymaster

Sure thing — more than once, I’ve been duped myself by missing something key because it was in the stimulus instead of the rules — as annoying as it is, hope you found it useful to be exposed to it — let me know if u ever need anything else — Mike

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