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 Jeremy Press
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#78978
Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination game, where the Identify the Templates approach can be used (but is not absolutely essential).

1. Since there are 8 potters' bowls, exactly 6 of which must be displayed in a row from 1 to 6, the base of the game is the 1 to 6 row, and the scenario should also display 2 "out" spots for the two potters' bowls that will inevitably not be displayed.

2. The first rule is a double-not arrow, showing that L's and M's bowls cannot be displayed simultaneously. In addition, one of the "out" slots should be filled by a dual option for L or M (since both cannot be displayed, at least one will have to be out).

3. The second rule is a conditional rule, with P's being both "next to" O and "next to" S as the necessary condition (notice the "only if" modifier). In "if-then" terms, the rule means that if P is displayed, then it must appear immediately beside both O and S. O and S could each be either right before or right after P in this construction. Don't forget, though, that the rule allows for the possibility that P is not displayed (in which case O and S would be "set free" to appear in any position relative to one another). There isn't a perfect way to represent the contrapositive of the rule, but think about the implications of the rule from a negative angle. If O were not displayed, then P could not be displayed. But this would "overload" the out group (since one of L or M must be out). That means O cannot be out, and therefore must be displayed. The same goes for S! This is the first major, and interesting (and most important!), inference of the game. The rule isn't done yielding inferences, though. Since every time P is displayed it has something immediately before and immediately after it, that means that P cannot be displayed in position 1 and P cannot be displayed in position 6.

4. The third rule is a conditional rule, with R's being on position 1 or 6 as the necessary condition (notice the "only" modifier). In "if-then" terms, the rule means that if R is displayed, then it must appear on position 1 or 6, meaning it can never appear in any of positions 2 through 5. Don't forget, though, that the rule allows for the possibility that R is not displayed (i.e., the rule only triggers if R is displayed).

5. The fourth rule is represented with Not Laws in the diagram for S beneath positions 2 and 4. The rule yields the interesting inference that P cannot be displayed in position 3, because if you tried to display P in position 3, that would force S to be in either position 2 or 4 (which the rule prevents).

6. The fifth rule is a conditional rule, with N's being on position 5 as the necessary condition (notice the "only" modifier). In "if-then" terms, the rule means that if N is displayed, then it must appear on position 5, meaning it can never appear in any of positions 1, 2, 3, 4, or 6. Don't forget, though, that the rule allows for the possibility that N is not displayed (i.e., the rule only triggers if N is displayed).

7. V is a random variable, denoted with an asterisk in the Global Diagram below.

8. The above rules present the possibility for identifying templates. The inferences surrounding P limit P's placement to either position 2, position 4, position 5, or being "out" of the game. Depending on your comfort level with creating templates, it could be worthwhile to build templates around these 4 options, displayed below.

Global Diagram
Setup December 2015 Game 2.png
Template Diagrams
Templates December 2015 Game 2.png
 Ari
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#78960
I would love to see the set up/explanation of this one. I feel like I could not decide if I wanted to draw out scenarios or not. I also didn't include V in much of my diagramming, but then multiple questions involved V and I felt like I missed something obvious. Help would be greatly appreciated! Thank you!
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 Stephanie Oswalt
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#79007
Jeremy has posted a full explanation above. Thanks! :)
 gwlsathelp
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#78996
Thank you, Jeremy! This was a fantastic breakdown of all the templates and deductions! I greatly appreciate this.
 VamosRafa19
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#82574
I'm not sure how to make the inference that O must be in. I got the question that asked about it later right by eliminating other answers, and then testing a couple of the remaining then it clicked but by first going through it I didn't quite pick that. Did you think about the contrapositive and just think what happens if P/S/O are each out, knowing that one of L/M needs to be out?
 Adam Tyson
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#82771
That's pretty much it, VamosRafa19! If either S or O were out, then P would also have to be out, and we would either not have enough variables to complete the game or we would be forced to violate the rule about L and M. Since we cannot do that, those two must both be in!
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 kmclean
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#86957
Hi Team!

Can you please review rule #1: when completing this I accounted for both L and M not being in at the same time. However, because two bowls are always out- can L and M both not be out at the same time?

TIA :-D
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 Dave Killoran
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#86963
Hi K,

Yes, according to the rule, La and M can both be out at the same time. And, from the way the game works, that can happen as well and not violate the remaining rules. Jeremy's note above is that since you always have to have at least one of the two out, you should reserve a slot for that since "at least one will have to be out." That does not affect the other slot, just fixes the minimum we know :-D

Thanks!
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 SGD2021
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#96090
Why is this rule (Serra's bowl cannot be displayed in either position 2 or position 4) interpreted as meaning S cant go in 2 OR S can't go in 4? How can we know in the future when it means No to both position 3 and 4 on a different game with a similar rule?
 Adam Tyson
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#96141
"Cannot be displayed in either" means prohibited from both, SGD. That's just the plain English meaning of the words. That can be a little confusing when compared to the positive form, "can be displayed in either," which would allow it to be in one position or the other. I'm no English teacher, but I suspect it's because "can" is permissive - you are allowed, but not required, so it's flexible - while "cannot" is prohibitive, which means you are absolutely not allowed, no matter what, and which is completely inflexible.

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