Diagram

[ArekS342]

Are there any specific deductions to this game? It seemed to me like a game that you mostly have to brute force. My strategy was to split the game board into 3 with Pang going Thursday, Friday, or both in each respective board. Is this the right strategy, or are there deductions to be made? Thank you!

[RomaG387]

Are there any specific deductions to this game? It seemed to me like a game that you mostly have to brute force. My strategy was to split the game board into 3 with Pang going Thursday, Friday, or both in each respective board. Is this the right strategy, or are there deductions to be made? Thank you!

There is at least one deduction that can be made - L has to be one of the Saturday's volunteers, although I don't recall this inference being directly useful during my take. With this in mind, I would have to agree with you that this game seems to prefer brute force. Questions 20 and 23 are huge time sinks , and being able to finish them on time seems to be dependent on our ability to go through the easier games (1 & 2) very quickly. I personally didn't split the game boards based on P - it seemed like there would still be too many possible scenarios. Instead, I just mentally noted that I have to see P on Thursday or Friday, or both.

[HirshaV851]

I definitely plugged and chugged through most of this one; seemed pretty back-end to me. What sort of helped me through some of these was noting that the distribution of elements has to be 2-2-2-2-1, and just keeping in mind that Q doesn't have any rules attached to it. The M-L rule was a mover in this game, so had to be aware of how that would play out in certain scenarios.

To any instructors reading this - mind putting up a diagram, as well as solutions to the questions? Thank you!

[puzzlep299]

5 people and 9 positions
rule 1 no one works every day
so 2-2-2-2-1
4 people works on 2 positions and 1 person works on 2 positions

(1) if only 1 L, MNPQ works on 2 positions, but rule 2: M-->L
so only 1 L doesn't work

(2) if 1 N
MQQ
L P M
P N L
4 5 6

(3) if 1 Q
MQN
L P M
P N L
4 5 6

(4)if 1 M
MQL L/Q Q LQN
L P Q N P M QPM
P N N P N L PN L
4 5 6 4 5 6 4 5 6

(5)if 1 P
Q/N Q N/Q NMQ
M P M QLM
L N L P NL
4 5 6 4 5 6

[TyroneC548]

I think I finally cracked this game -- that is, found an easy setup


Essential Rules & Inferences :

Rule 1: A person can occupy at max 2 positions: Inference: Since we have 5 people and nine slots, the breakdown will be 2-2-2-2-1
Rule 2. M --> ML Inference: you cannot have one L because that would mean one M, which contradicts the inference above. Further inference: you must have 2 Ls
Rule 3 (technically the fourth listed on the game): the pool of persons for Saturday is LMNQ. Inference: L must work Saturday, since NQM would contradict rule 2.

Big Inference: Combining Rule 2 and 3 above, we know that L works Thurs and Sat OR Friday and Sat, which gives us the game board below (remembering the rule, not listed above, that N works Friday):

L: Fri/Sat

__ L L
__ __ __
__ N __

OR

L: Thurs/Sat

L __ L
__ __ __
__ N __


Since we know we cannot have three Ls and that putting an M where an L is not present will give us three Ls, on whichever day L can't work in the frames above (Thursday and Friday, respectively), we will have PNQ as the pool of available workers for that day. As such, we have the following setup:

L: Fri/Sat

N L L
P __ __
Q N __

OR

L: Thurs/Sat

L P L
__Q __
__ N __

For the "NLL" game board above, we see that we already have 2 Ns in Thursday and Friday, respectively, so we know N cannot work Saturday. Since P also cannot work Saturday, we end up with only MQ left to work Saturday alongside L :

L: Fri/Sat

N L L
P __ M
Q N Q

Since we now have 2 Qs, in the middle blank we must have either M or P:

L: Fri/Sat

N L L
P M/P M
Q N Q

As for the remaining "LPL" frame (two examples) above, we know that MPNQ are available to work Thursday (so two of the four) and MNQ are available to work Saturday (so two of the three). However, we also know that QN are already working Friday, which means that QN cannot work Thursday, since that would leave only M to work Saturday. In this way, for Thursday for the "LPL frame," the options are M P N/Q, which gives us the following diagram:

L: Thurs/Sat

L P L
M Q __
P N __

AND

L P L
M/P Q __
N/Q N __

So, in the end, we have 3 frames:

L: Thurs/Sat

L P L
M Q __
P N __

AND

L P L
M/P Q __
N/Q N __

OR

L: Fri/Sat

N L L
P M/P M
Q N Q


For the blanks in the "LPL" frame its just a matter of figuring out which two of MNQ can be placed in the two remaining spots.

Let me know if this explanation is sound!

[ReginaP412]

Still not getting this game/set up. Do any teachers have a PDF version of the diagram for this? Thank you!

[Laura Damone]

Sure thing! Posting as a Google Doc. Be sure to check out the "Understanding the Notation" part of the doc, beneath the diagram and notes, so you can see the thought process step by step. I only needed to draw three hypos for this game, only one of which was testing an answer, so not much "brute force" at all, actually! The key to this game is the aforementioned L on Sat inference, explained further in the doc, and the numeric distribution.

Hope it helps!

https://docs.google.com/document/d/1F3X ... sp=sharing

[ChentuoZ54]

It is better to draw a pattern like this:

L M N P Q
T __ __ __ __ __
F __ __ Y __ __
S __ __ __ X __

here Y=yes, X=NO

if M=Y , then L=Y

NO something like:
T ...a...
F ...a...
S ...a...
, where a can be L/M/N/P/Q.

and you just need to remember that there 3 Y and 2X in each row.