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 nadiaguo
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#2573
How would you set up this game ?

I did

1st year _ _ _
2nd year_ _ _
...
6th year _ _ _

because I deduced that it would take 6 years to complete a cycle. Is this correct?

I also wasn't really sure how to diagram the rules..
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 Dave Killoran
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#2574
Hey Nadia,

That's the Clan game, correct? Take a look at that again because it is a 5 year cycle, not 6 (5 clans x 3 participations each). So it looks like:

1st year _ _ _
2nd year_ _ _
3rd year _ _ _
4th year_ _ _
5th year _ _ _

The key rules are the "once every two years" and the "no three in a row" rules. Regardless, it is a tough Pattern game.

Let me know if that helps. Thanks!
 jared.xu
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#2638
Hey Dave,

I hope you don't mind me asking another question about this game on this blog. I actually just listened to Jon Denning's virtual module on Pattern Games I, which features this game. And I understand how we would come up with the five possible placements for each clan. But I have a question regarding how we would know that each clan must follow each of the five distinct patterns only once. For instance, if N follows 1-3-5, O must not follow that pattern again. Of course, we could take the time to draw out a hypothetical to see that it does not work. But is there some clue that would tell us that each one of the five possibilities must be used by one of the clans, that they are not mere "possibilities" but each a pattern that must be carried out by one of the clans? I am asking this because questions 19 and 21 seem to require us to notice this fact. I was somewhat surprise when Jon solved the two questions assuming that we already know this fact. Thank you in advance for replying.

Jared
 Jon Denning
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#2639
Hey Jared - thanks for the question. The answer to it is simply that the mathematics of the distribution--where each of the five years has three clans, and each of the five clans is used exactly three times--require you to have five unique patterns/orders.

Consider them:

1-3-5
1-3-4
1-2-4
2-3-5
2-4-5

Now think what would happen if you took one of the non 1-3-5 orders, say 1-3-4, and made it into another 1-3-5: only two clans would be in the fourth year (1-2-4 and 2-4-5), and four clans would now in the fifth year (1-3-5, 1-3-5, 2-3-5, 2-4-5). This violates the rules. The same is true of duplicating any of the other orders.

Or you could think of it this way. Imagine the three clans for year 1. How can those three be placed? One could go again in year 2, so it would have to be 1-2-4. And that's the set order for that clan. The other two must go year 3 (can't be more than two years apart), so 1-3-4 and 1-3-5. And those are the set orders for the other two. Why can't they both be 1-3-4? Because then you'd have finished with all the year 1 clans by year 4 (1-2-4, 1-3-4, 1-3-4), and only have two remaining clans for year 5. Since you need three clans for each year, two 1-3-4 orders won't work. And this mathematical logic applies to each of the clans/orders given.

I hope that helps!
 nadiaguo
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#3040
Thanks, your response to my question helped a bunch.

Do you really need to know the patterns to solve this game? I feel like it just creates more confusion, as the questions the other guy mentioned can totally be solved just by using process of elimination
 Jon Denning
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#3042
I think that depends. They definitely help, but certainly you could get through the game without them by simply understanding the rules and restrictions that create the patterns. Would it take a little longer without recognizing the patterns? Probably. Are they absolutely necessary for completing the game? No, probably not.
 ValVal
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  • Joined: Jul 05, 2017
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#43498
Hey guys! Can anyone help me with the detailed set up for the game? I feel like I still missing some key inferences, and I cannot solve it, even using numerical distribution. Thanks!
 Adam Tyson
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#43641
The five patterns Jon set up earlier in this thread IS the detailed setup of this game, ValVal! That's one thing about pattern games that makes them such a pain in the neck challenge - the lack of a truly robust setup, just a rough idea of what can and cannot happen.

Try a hypothetical situation, which is one way that we often attack pattern games. We aren't trying to come up with every solution, but just to get a sense of how it all works. Another strategy is to look at the first question to give you some clues, so if I were playing with a hypo in this game I would base it on the first question, possibly helping me answer it at the same time that I get my brain wrapped around the patterns. Here we go!:

Year one: NOP

Year two: I need the other two, S and T, to participate, per the first rule, and one of the first three will have to repeat. At this point, you will have noticed that you have already answered the first question, because only answer E has both S and T in it! So I will go with OST as my Year 2 pattern

Year 3: O is out, because it can't go three years in a row (rule 2), and N and P are back in because they have to be there in any two year cycle (rule 1 again). So Year 3 is NP and let's say S

Year 4: S can't go three in a row, so it's out, and O and T are back in. How about we try P sticking around this time, so Year 4 is OTP.

Now pay attention to the last rule here! No clan can go more than three times in a cycle, and P and O just both had their third turn in the harvest ceremony. They have to be out for Year 5, and that means my Year 5 will have to be TSN. Let's recap:

1. NOP
2. OST
3. NPS
4. OTP
5. TSN

In any two year period, all five of our variables were used. Rule 1 is satisfied.

Nobody went three years in a row. Rule 2 is satisfied.

Everyone went three times, so the cycle ends and we can start another one. Rule 3 and 4, which aren't really rules so much as restrictions, are telling us we have finished the cycle and can start anew. That answers question 20!

Nobody went more than 3 times total. Rule 5 is satisfied.

Let's compare this to Jon's numeric description of the patterns. N is my 1-3-5 variable, meaning it appeared in years 1, 3 and 5. P is my 1-3-4. O is the 1-2-4 variable, appearing in those years. S is the 2-3-5, and T is the 2-4-5.

Now, you could swap these variables around many different ways. Make T the 1-3-5, and O the 1-3-4, and so on. As long as you follow that numeric pattern, assigning one letter to each pattern, you will have a viable solution. How many solutions are there? I don't even want to take the time to do the math, but it's a lot. Okay, I do want to do the math, and it's 120 possible solutions. You do NOT want to go after all of those! Instead, you want to uncover the patterns, get a sense of how the game is supposed to work, and then dive on into the questions. You may find that the questions are mostly about understanding the patterns and are not about the solutions at all!

That was a lot, and I do not mean to suggest that pattern games cannot have a clear setup, just that they are frequently not about the setup as they are about just uncovering and understanding the patterns. Hypotheticals take time, but they tend to be worth it on these games if they lead to a greater understanding. Give that a try and see how it shakes out! Good luck!
 Patrice M. Walker
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  • Joined: Dec 08, 2020
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#84367
Hey,
So for this question the pattern that has me a little stuck is the 1-3-5. The rule says each candidate must be selected once on any two consecutive days. In the 1-3-5 pattern there are no consecutive days but then when this pattern is used everything comes together in the rules. HOW?
Am I reading the rule wrong and how do I make sure I do not make that mistake again?

I believe coming up with the patterns are essential to completing pattern games on time however, this is truly a...challenge for me.
 Jeremy Press
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#84390
Hey Patrice,

So I think you're misreading the first rule, which says, "Each clan must participate at least once in any two consecutive years." That means for any two-year period, a clan has to show up at least one time. So, for the clan that goes in years 1, 3, and 5, it's showing up once in the two-year period that includes Year 1 and Year 2 (in year 1). It's also showing up once in the two-year period that includes Year 2 and Year 3 (in year 3). It's also showing up once in the two-year period that includes Year 3 and Year 4 (in year 3). And it's showing up once in the two-year period that includes Year 4 and Year 5 (in year 5). That satisfies the rule, because that's every possible combination of two consecutive years.

The way to avoid misreading any rule is to give effect to the language of every word in the rule, and to consider rearranging the language of the rule. How could you rearrange the language of this rule to help understand it better? Try putting the "any" clause first in the sentence: "In any two year period, each clan must participate at least once." So, when I look at a two-year period (say, Years 1 and 2), I should see a clan participating at least one time.

Also think about what the rule would say if it were doing what you read it to do: it would say, "At least once, each clan participates in two consecutive years." That would mean, for every clan, there would have to be at least one occasion in the game where it participated in two consecutive years. Different wording than our game rule.

I hope this helps!

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