# Dominion Strategy Forum

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### AuthorTopic: Logic Riddles  (Read 4817 times)

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#### sitnaltax

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##### Re: Logic Riddles
« Reply #25 on: April 29, 2015, 10:54:12 pm »
+1

I have used the number 3 twice to reflect the fact that I also used that number twice when counting for the clue, apparently. My shame is immense.

So that means I got it completely right!

Indeed.  Remind me not to make any real life decisions that require critical thinking after between the hours of 11 PM-9 AM.
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#### GeoLib

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##### Re: Logic Riddles
« Reply #26 on: April 29, 2015, 11:13:11 pm »
0

Without looking at the clues or discussion. This isn't optimized, but it works (I think):

There are only two hand placement positions, adjacent and opposite.

1. Allow a round to pass without touching anything, to confirm that they don't all start the same.
2. Place hands adjacent.
If you get two of the same orientation,
then flip both. Now you either win, or there are three of the same orientation remaining

else (you get two with different orientations)
flip them so they're the same. Either you win, or there's at least one of the other orientation.
3. Place hands opposite. One of the bowls you get is guaranteed to be one from the previous step. If the other is in the same orientation, then flip nothing. You have three bowls in the same orientation. If the other is in the opposite orientation, flip it so now it's the same. Either you win or you have three bowls in the same orientation.

3/4. Place hands adjacent again. Either you get the single remaining in the opposite orientation, flip it and win. Otherwise, you get two in the same orientation. Flip 1.
4/5. Now there are two pairs in the same orientation. Place hands opposite. If you get two of the same orientation, flip both and win, otherwise there are two pairs of adjacent bowls with the same orientation. Flip nothing.
5/6. Place hands adjacent. If you get two of the same orientation, flip both and win. Otherwise, flip both.
6/7. Now there are two pairs of opposite bowls with the same orientation. Place hands opposite. Flip both and win.

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#### scott_pilgrim

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##### Re: Logic Riddles
« Reply #27 on: April 29, 2015, 11:16:14 pm »
+1

I'm pretty bad at solving these, but I love reading about them and presenting them. I was about to post my favorite, but I seemed to recall doing so already. Found it:

http://forum.dominionstrategy.com/index.php?topic=6426.0

Damn. I even looked (searched for "riddles", because I quickly found sudgy's recent post about pen-and-paper logic puzzles) but didn't go back this far. Good stuff there, including some of the ones I had meant to post.

My favorite follow-on to the blue eyes/brown eyes problem, although one that I don't have a good handle on myself: Why does the Guru making a statement that everyone already knows is true matter? If he had come in and said "Bacon is delicious", would that have had the same effect? Why not, given that it added no new information?

You don't care about the information you get from that, but you care about the information it gives everyone else.  It serves as the base case for the induction.  You know there's someone with blue eyes.  You know that everyone knows there's someone with blue eyes.  You know that everyone knows that everyone knows there's someone with blue eyes.  Etc., until you get x layers deep, where x is the number of people with blue eyes, and then you get stuck.  Everyone has to be able to assume that everyone knows that everyone knows that everyone knows that (...) everyone knows that someone has blue eyes, and you can only make that assumption when that statement is made.

Saying "Bacon is delicious" wouldn't have helped because everyone already knew that everyone knew that everyone knew that (... infinitely) everyone knew that bacon is delicious.  Also, there is no induction to be done from that base case.
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#### GendoIkari

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##### Re: Logic Riddles
« Reply #28 on: April 30, 2015, 03:17:33 pm »
+1

I'm pretty bad at solving these, but I love reading about them and presenting them. I was about to post my favorite, but I seemed to recall doing so already. Found it:

http://forum.dominionstrategy.com/index.php?topic=6426.0

Damn. I even looked (searched for "riddles", because I quickly found sudgy's recent post about pen-and-paper logic puzzles) but didn't go back this far. Good stuff there, including some of the ones I had meant to post.

My favorite follow-on to the blue eyes/brown eyes problem, although one that I don't have a good handle on myself: Why does the Guru making a statement that everyone already knows is true matter? If he had come in and said "Bacon is delicious", would that have had the same effect? Why not, given that it added no new information?

Scott's answer is correct. But man, even after I thought I'd fully understood the blue-eyes problem, I spent quite a while trying to understand how it was possible that the guru's statement could affect anything. Because not only does everyone know that the guru can see someone with blue eyes (because each person sees someone with blue eyes), but everyone knows that everyone knows that even! So it just seemed like the statement was 100% meaningless. I finally got it though, by thinking about the case where there's only 3 blue-eyed people. In that case, all 3 know there's a blue-eyed person, and all 3 know that everyone knows there's a blue-eyed person. But all 3 do NOT know that everyone knows that everyone knows. Wikipedia explains it here: http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29
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#### popsofctown

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##### Re: Logic Riddles
« Reply #29 on: April 30, 2015, 03:24:25 pm »
0

oh, any two compass points.  For some reason I just assumed east and west because that's what would be comfortable for your arms haha.
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#### Witherweaver

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##### Re: Logic Riddles
« Reply #30 on: April 30, 2015, 03:27:50 pm »
0

I'm pretty bad at solving these, but I love reading about them and presenting them. I was about to post my favorite, but I seemed to recall doing so already. Found it:

http://forum.dominionstrategy.com/index.php?topic=6426.0

Damn. I even looked (searched for "riddles", because I quickly found sudgy's recent post about pen-and-paper logic puzzles) but didn't go back this far. Good stuff there, including some of the ones I had meant to post.

My favorite follow-on to the blue eyes/brown eyes problem, although one that I don't have a good handle on myself: Why does the Guru making a statement that everyone already knows is true matter? If he had come in and said "Bacon is delicious", would that have had the same effect? Why not, given that it added no new information?

Scott's answer is correct. But man, even after I thought I'd fully understood the blue-eyes problem, I spent quite a while trying to understand how it was possible that the guru's statement could affect anything. Because not only does everyone know that the guru can see someone with blue eyes (because each person sees someone with blue eyes), but everyone knows that everyone knows that even! So it just seemed like the statement was 100% meaningless. I finally got it though, by thinking about the case where there's only 3 blue-eyed people. In that case, all 3 know there's a blue-eyed person, and all 3 know that everyone knows there's a blue-eyed person. But all 3 do NOT know that everyone knows that everyone knows. Wikipedia explains it here: http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29

Crazy how logic do that.
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#### enfynet

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##### Re: Logic Riddles
« Reply #31 on: April 30, 2015, 03:33:03 pm »
+1

A Farmer needs to cross a river with his goat, his wolf, and his cabbage...

...to get to the chicken on the other side.
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#### liopoil

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##### Re: Logic Riddles
« Reply #32 on: April 30, 2015, 04:36:46 pm »
0

I prefer the generalized eyes problem. The Guru comes in and says, "Of you x people, there are not exactly n of you with blue eyes, for x >= n". No matter the values of x, n, and the actual number of people with blue eyes, everyone eventually leaves. The original problem is the case (100, 0, 100), if I remember correctly.