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Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

math.dartmouth.edu

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Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#41

Post by millstone »

gowld wrote: post #32
millstone wrote: post #21

In the Dot-town suicides, say the stranger says "Alice has a blue dot." Alice then kills herself. Why would the other residents die? I think this satisfies the requirements: there's certainly some number of blue dots for which the statement would be false, namely zero.

That's not what the author intended by "anything about the number of blue dots". The author means "anything about the number of blue dots, but not who has them", because the proof of the solution relies on the fact that each person ("Alice") doesn't know whether their own dot is in the set the stranger speaks about but everyone else does know whether "Alice" is in the set. "Alice has a blue dot" adds extra informatio…

I think that's right. So the author's description of "anything non-trivial" is weakened to "anything non-trivial maintaining information symmetry", which feels constricting, certainly no longer "frighteningly general."

This also reveals a strategy for townsfolk who wish to survive: simply inform a blue-dot of their color, breaking the logic chain. That winning move ought to factor into the strategy of these perfect logicians!

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#42

Post by cortesoft »

anyfoo wrote: post #37
cortesoft wrote: post #30

Earlier quoted context omitted.

Right, but if there were two red dots the town is fine. In a one red dot town, you could say “there is at least one blue dot”

Would they be fine? So let's say there are two people with red dots, let's name them Ruth and Rudy. Ruth now knows that "not all dots are blue" (which is equivalent to "there is at least one red dot"). She sees Rudy with the red dot: Fine, here's the person with the red dot. But wait a minute, why is Rudy not killing himself? If Rudy is the only person with a red dot, he should have seen only blue dots... however he…

Ok now it is making sense. The same would be true if you went to three dots.... the third person would think, “wait, why aren’t the two blue dotted people killing themselves? There must be a third blue dot... wait, the third blue dot must be me”

That makes sense. What about the other commenter, who said something like “Alice has a blue dot.”

Wouldn’t that not lead to everyone’s death?

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#44

Post by ink_13 »

zawerf wrote: post #40

Where can I find more of these? Do you guys recommend this author's books such as https://www.amazon.com/Mathematical-Puzzles-Connoisseurs-Pet... ? (It's hard to find the right search term for this that doesn't return a lot of non-mathematical brainteasers or stuff aimed at kids)

Winkler's book looks pretty good, yes.

You'd probably also enjoy the works of Martin Gardner, who wrote a recreational mathematics column in Scientific American for 25 years, which has been collected across many volumes.

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#45

Post by uiri »

cortesoft wrote: post #42
anyfoo wrote: post #37

Earlier quoted context omitted.

Would they be fine? So let's say there are two people with red dots, let's name them Ruth and Rudy. Ruth now knows that "not all dots are blue" (which is equivalent to "there is at least one red dot"). She sees Rudy with the red dot: Fine, here's the person with the red dot. But wait a minute, why is Rudy not killing himself? If Rudy is the only person with a red dot, he should have seen only blue dots... however he…

Ok now it is making sense. The same would be true if you went to three dots.... the third person would think, “wait, why aren’t the two blue dotted people killing themselves? There must be a third blue dot... wait, the third blue dot must be me” That makes sense. What about the other commenter, who said something like “Alice has a blue dot.” Wouldn’t that not lead to everyone’s death?

I think that "Alice has a blue dot" is technically not a statement about the number of blue dots.

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#46

Post by qz3 »

hyperpape wrote: post #2

Problem 7 has an even more fiendish counterpart: https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever .

Very interesting, but incredibly complex. I'm tempted to make a python implementation to play around with for better understanding.

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#48

Post by keithnz »

HanayamaTriplet wrote: post #23
scrooched_moose wrote: post #7

Earlier quoted context omitted.

To get super pedantic, even if that was the case you could use a lock out tag out type device to still attach two locks. https://www.media-partners.com/upload/i20121017160441/img1.j...

Another alternative would be to thread a small steel cable with looped ends large enough for two locks through the eye and then lock the loops together.

the problem is if you introduce new things, then you can solve it like

1. Bolt Cutters 2. Break the box 3. Send the key design via the internet and a link to https://www.youtube.com/watch?v=8M-HYptOMJI

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#49

Post by mikenew »

Spent quite a while on the Wimbledon problem before giving up and reading the answer. But the answer is wrong, because they don’t play tiebreakers at Wimbledon (or any of the grand slams besides the US Open). Pretty frustrating TBH. Kind of felt the same about the padlocked boxes one too, although at least that one is more just a little ambiguous vs outright wrong.

Re: Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

#50

Post by arachnids »

mikenew wrote: post #49

Spent quite a while on the Wimbledon problem before giving up and reading the answer. But the answer is wrong, because they don’t play tiebreakers at Wimbledon (or any of the grand slams besides the US Open). Pretty frustrating TBH. Kind of felt the same about the padlocked boxes one too, although at least that one is more just a little ambiguous vs outright wrong.

They don't play tiebreakers in the fifth set. All other sets work normally. The answer is correct because it's only talking about the first three sets.
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