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The Resistance» Forums » General

Subject: Logic Puzzles for The Resistance rss

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Derek Thompson
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I'm intending to have students play this in a Discrete Math course I'm teaching and then give them the following assignment. If you see any problems or have cleverer puzzles than these, please please share!

Thanks

Derek

The Resistance Puzzles:

Amanda, Bob, Carla, Derek, Ellie, and Fred are playing a few six-player games of the Resistance. There are two spies in each game. The number of players on each mission is 2, 3, 4, 3, 4.

In these first three scenarios, you are asked to identify some players' identities. Write a sound, valid argument justifying your answer once you have figured out the answer. Remember – only spies can play fail cards!

Game 1:
Amanda and Bob go on the first mission. One Fail card and one Success card appear.
Carla, Derek, and Fred go on the second mission. One Fail card and two Success cards appear.
Who is definitely a Rebel (not a Spy)?

Game 2:
Amanda and Derek go on the first mission. Two Success cards appear.
Carla, Fred, and Derek go on the second mission. One Fail card and two Success cards appear.
Derek, Bob, Ellie, and Amanda go on the third mission. Two fail cards and two Success cards appear.
Who is definitely a Spy?

Game 3:
This time, the players agree to a new rule: when voting on a mission, Spies vote yes if and only if a Spy is on the proposed team. All other information from above is the same. The voting for round one went like this:
--------|Team 1-----|Team 2
-------|Amanda/Derek|Bob/Derek
Amanda-|Yes---------|Yes
Bob----|No----------|No
Carla--|No----------|Yes
Derek--|No----------|No
Ellie--|No----------|No
Fred---|No----------|No
A team hasn’t been picked yet, but Derek yells that he knows exactly who the two spies are. Who are they?

For the fourth scenario, you can make one assumption. Pick one player and state what you assume their identity to be, and from there, make an argument that identifies everyone’s identity (you can do this quickly by simply stating who the two spies are). In other words, write a valid argument that is sound if your assumption is true, but is still valid even if the assumption is false.

Game 4:
Amanda and Bob go on the first mission. Two Success cards appear.
Amanda, Bob, and Carla go on the second mission. One Fail card and two Success cards appear.
Amanda, Derek, Ellie, and Fred go on the third mission. One Fail card and three Success cards appear.
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Pasi Ojala
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You are leaving out information about who suggested each team.
1.
Spoiler (click to reveal)
Ellie - the only one not in failed quests, while both spies were

2.
Spoiler (click to reveal)
Derek - Carla and Fred can not be spies, because both spies were on M3, and thus Derek failed M2

3.
Spoiler (click to reveal)
Derek claims Ellie and Fred to be spies, which is why that kind of agreement should not be done.

4. You really need to pick carefully to make it work, probably also assume that spies do not float missions.
 
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Derek Thompson
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a1bert wrote:
You are leaving out information about who suggested each team.
1.
Spoiler (click to reveal)
Ellie - the only one not in failed quests, while both spies were

2.
Spoiler (click to reveal)
Derek - Carla and Fred can not be spies, because both spies were on M3, and thus Derek failed M2

3.
Spoiler (click to reveal)
Derek claims Ellie and Fred to be spies, which is why that kind of agreement should not be done.

4. You really need to pick carefully to make it work, probably also assume that spies do not float missions. (I suggest you fix Amanda to be a spy, then try to figure out the other spy.)


I might have made the last directions unclear - I'm saying if they choose any player and assume them to be a spy, for example, they can then necessarily deduce the other spy....

These are of course pretty simple - glad you solved them and got the same answers I did

I wonder how difficult of puzzles can be made?

Yes, I did leave out who suggested each team, as I'm trying to make thoroughly mathematical puzzles even though Resistance is largely done by social deduction, since good players usually wouldn't allow for scenarios like those listed.

Thanks

Derek
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Dok Indigo
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Answers in spoiler tags
Spoiler (click to reveal)

Game 1: Ellie
Game 2: Derek
Game 3: Ellie, Fred
Game 4:
Assumption:
A (or B) spy: second spy not known
A (or B) rebel: one spy between B and C (A and C), one spy between D, E, F (A, D, E, F)
C spy: B rebel, second spy between A, D, E, F
C rebel: one spy between A, B, one spy between A, D, E, F
D spy: second spy between A, B, C
D rebel: one spy between A, B, C, one spy between A, E, F
E spy: spy A, B, C
E rebel: spy A, B, C and A, D, F
F spy: spy A, B, C
F rebel: spy A, B , C and A, D, E
 
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Spoiler (click to reveal)
missed something
B spy: other spy A, D, E, F
B rebel: spy A, C and A, D, E, F
 
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aldaryn wrote:
I wonder how difficult of puzzles can be made?

I'm more fluent in 5-player games.

This kind of puzzling is going on when you play Resistance in IRC. Of course the best spies are so good that you can't be certain by just FAILed mission results, but sometimes you can be certain that someone definitely is good.
 
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Derek Thompson
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a1bert wrote:
aldaryn wrote:
I wonder how difficult of puzzles can be made?

I'm more fluent in 5-player games.

This kind of puzzling is going on when you play Resistance in IRC. Of course the best spies are so good that you can't be certain by just FAILed mission results, but sometimes you can be certain that someone definitely is good.


I'm open to any puzzles you guys can think of! Trickier the better...
 
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Jorgen Peddersen
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You can create some very interesting logic puzzles by introducing the Plot cards. I don't have time to craft one, but the ones where you must reveal your identity to another player gives you an implication argument between the two players. You'd need to add a 7th player to get some of these interesting ones in, but you could have stuff like:

Derek draws Establish Confidence and shows his card to Ellie. Ellie claims Derek is not a spy.

This, of course, gives you "If Derek is a Spy, Ellie is a Spy" implication which you can craft some fine logical proofs out of.
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Derek Thompson
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Clipper wrote:
You can create some very interesting logic puzzles by introducing the Plot cards. I don't have time to craft one, but the ones where you must reveal your identity to another player gives you an implication argument between the two players. You'd need to add a 7th player to get some of these interesting ones in, but you could have stuff like:

Derek draws Establish Confidence and shows his card to Ellie. Ellie claims Derek is not a spy.

This, of course, gives you "If Derek is a Spy, Ellie is a Spy" implication which you can craft some fine logical proofs out of.


Thanks for the idea!

Derek
 
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aldaryn wrote:
Clipper wrote:
You can create some very interesting logic puzzles by introducing the Plot cards. I don't have time to craft one, but the ones where you must reveal your identity to another player gives you an implication argument between the two players. You'd need to add a 7th player to get some of these interesting ones in, but you could have stuff like:

Derek draws Establish Confidence and shows his card to Ellie. Ellie claims Derek is not a spy.

This, of course, gives you "If Derek is a Spy, Ellie is a Spy" implication which you can craft some fine logical proofs out of.


Thanks for the idea!

Derek


As an extension of this, you would probably find the Lady of the Lake/Inquisitor power to be good at crafting more complex logical possibilities.

Part of the reason this element makes the game harder for spies is that spies don't always follow the logic to the necessary conclusion. They forget to assume that they themselves are rebels, and so the logic isn't obvious to them. When someone should know something logically, and doesn't, it's evidence that they are up to no good.
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aldaryn wrote:
These are of course pretty simple


I sent a few minutes thinking about problem 3 and couldn't work it out. Now that I know the answer it seems fairly simple.

Adding plot cards or possibly Avalon roles (and not worrying if some of the scenarios you create might be a certain win for the bad guys due to Merlin being revealed).
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Eugene Wong
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This thread is old, but I do enjoy the logic aspect of Resistance. It becomes a real life brain teaser.

###

### Game #1 ###

Spoiler (click to reveal)
Ellie.


### Game #2 ###

Spoiler (click to reveal)
Derek.


It seems that there is another question that you could ask about Game #2.

Spoiler (click to reveal)
Who are definitely rebels?
Spoiler (click to reveal)
Carla and Fred.


### Game #3 ###

Spoiler (click to reveal)
Bob, and Carla? Derek knows that he isn't a spy, and nobody approved the first mission, other than Amanda. I think that it takes a spy to know a spy, and Carla didn't approve the first team.

### Game #4 ###

I am not sure how this works. I'll try 2-3 answers anyways.

Spoiler (click to reveal)
1) Amanda is a rebel: spies are Bob, and Derek. The same accusation could be made against Carla, and Ellie.
2) Bob is a rebel: spies are Amanda, and Derek.

This doesn't seem difficult. Am I missing something?


###

As an extension of Game #2's question, here is a question that I have.

Spoiler (click to reveal)
If 2 fail cards can be used to reveal a spy, then what are the simplest statements can we make to discover spies in games with more spies?
[o]1) All the spy cards must be played in a mission.
2) If there are more mission team members than there there are spies in the game, then a Ven diagram could be used with that failed mission and another failed missions to identify the spy. The overlap in players is an indication of who is a spy.

[That was the easiest way that I could describe it, while trying to be accurate.]


###

Regarding Lady Of The Lake and Plot Cards, we can ask about role revelations.

1) What role card statements can be said about any 2 players before roles are revealed?

We can say these 4 statements.
* rebel-rebel
* spy-rebel
* rebel-spy
* spy-spy

2) What role card statements can be said about any 2 players after the second player tells us that the first player is a spy.

Spoiler (click to reveal)
We can say these 3 statements.
* spy-rebel
* rebel-spy
* spy-spy
All we did was remove the first combination of the original 4. Under normal circumstances, a rebel would not accuse a rebel.


3) What role card statements can be said about any 2 players after the second player tells us that the first player is a rebel?

Spoiler (click to reveal)
We can say these 3 statements.
* rebel-rebel
* rebel-spy
* spy-spy
All we did was remove the second combination of the original 4. Under normal circumstances, a rebel would not vouch for a spy.


4) What role card statements can be said about any 2 players after the second player tells us that the first player is a rebel, and then go on a failed 2p mission?

Spoiler (click to reveal)
We can say these 2 statements.
* rebel-spy
* spy-spy
All we did was remove the first combination of the previous 3. Under normal circumstances, a rebel would not vouch for a spy, and he can never play a fail card.

 
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Eugene Wong
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I see that there are 2 answers for Game #3. I wonder if both are correct.

I looked over the question again, and it might depend on the wording. If the spies must approve, when a spy is on the team, then other answer is correct. If the spies are allowed to approve only when a spy is on the team, but are not required to, then there is more than 1 answer.

I think that my answer is wrong, with the intended question. It was still fun, though.
 
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eugenetswong wrote:
I see that there are 2 answers for Game #3. I wonder if both are correct.

I looked over the question again, and it might depend on the wording. If the spies must approve, when a spy is on the team, then other answer is correct. If the spies are allowed to approve only when a spy is on the team, but are not required to, then there is more than 1 answer.

I think that my answer is wrong, with the intended question. It was still fun, though.


for reference:
--------|Team 1-----|Team 2
-------|Amanda/Derek|Bob/Derek
Amanda-|Yes---------|Yes
Bob----|No----------|No
Carla--|No----------|Yes
Derek--|No----------|No
Ellie--|No----------|No
Fred---|No----------|No

For game 3, I believe it is intended that spies must vote yes if there is a spy, and must vote no if there isn't a spy.

Spoiler (click to reveal)
After proposal 1, we know that Amanda and Derek are rebels.

(We know this because if there is a spy on the mission, there need to be at least 2 yes votes.)

After proposal 2, we know Bob and Carla are also rebels.

(If bob is a spy, he would need to vote yes. Since bob isn't a spy (and derek isn't a spy), if spyCarla wouldn't be allow to vote yes. So she isn't a spy.)



In the event they are only allow to vote yes when a spy is on the mission.

Spoiler (click to reveal)
proposal 1 tells us nothing.
Proposal 2 tells us:
If amanda is a spy, bob or derek is the other.
If carla is a spy, bob or derek is the other.

So this rule outs that amanda and carla are both spies.

So, from RebelDerek POV:
If bob is a rebel, Ellie and Fred are spies.
If bob is a spy, Amanda or Carla is the other spy.

And I'm pretty sure that it ends there, which leads me to believe this is the incorrect interpretation of the question.
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