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

math.dartmouth.edu

21–30 of 146 posts

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

#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.

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

#22

Love in Kleptopia needs to be explained better. The problem can only be solved if you can afix two padlocks onto a box, and I was presuming the lock box had a single, normally shaped padlock eye, which would make such a thing impossible. I find this happens a lot with "thought" problems: I can't solve it (and can often prove that) because the rules of the problem are inadequately explained.

I haven't looked at the solution but I don't see why it requires a box that can have two padlocks attached. A sends their open padlock and a box to B. B puts their open padlock in the box, and locks it with A's padlock and sends it back. A opens his padlock, puts the ring inside, locks it with B's padlock and sends it back. Maybe it was just too hard for you? :P

> A sends their open padlock and a box to B

And they are both promptly stolen, because neither is inside a padlocked box. "anything sent through the mail will be stolen unless it is enclosed in a padlocked box". Anything includes padlocks and boxes. In fact, even the padlocked box would be stolen because it's not inside a padlocked box. And if it were, the outer box would just be stolen. The puzzle as written is just turtles all the way down.

The proper form of the riddle would be that anything except for a padlocked box will be stolen from the mail.

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

#23

Love in Kleptopia needs to be explained better. The problem can only be solved if you can afix two padlocks onto a box, and I was presuming the lock box had a single, normally shaped padlock eye, which would make such a thing impossible. I find this happens a lot with "thought" problems: I can't solve it (and can often prove that) because the rules of the problem are inadequately explained.

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.

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

#24

Love in Kleptopia needs to be explained better. The problem can only be solved if you can afix two padlocks onto a box, and I was presuming the lock box had a single, normally shaped padlock eye, which would make such a thing impossible. I find this happens a lot with "thought" problems: I can't solve it (and can often prove that) because the rules of the problem are inadequately explained.

I initially had considered two padlocks being on the box, but ruled it out because "come on, that would just bring more attention to it such that they'd spend enough to break our measures".

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

#25

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.

Yeah, I was thinking about if the stranger said something like, “not all the dots are blue.” This is non-trivial by the definition given, and no one would have to kill themselves at all.

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

#26

Love in Kleptopia needs to be explained better. The problem can only be solved if you can afix two padlocks onto a box, and I was presuming the lock box had a single, normally shaped padlock eye, which would make such a thing impossible. I find this happens a lot with "thought" problems: I can't solve it (and can often prove that) because the rules of the problem are inadequately explained.

Also, the problem assumes that padlocked boxes themselves are not stolen. Presumably we're expected to consider this a reasonable assumption, because a thief wouldn't bother stealing a box that they couldn't open. But just as with public-key cryptography, a thief who can both steal packages and forge return addresses could intercept the box, place their own padlock on it, and then execute the rest of the protocol to perform a classic man-in-the-middle attack.

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

#27

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.

Yeah, I was thinking about if the stranger said something like, “not all the dots are blue.” This is non-trivial by the definition given, and no one would have to kill themselves at all.

"not all the dots are blue" - in the case where there are n people with n-1 blue dots and 1 red dot, the person with the red dot kills themself, and then everyone else kills themselves because they know that the red dot person killed themself because they did not see any red dots.

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

#28

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.

Yeah, I was thinking about if the stranger said something like, “not all the dots are blue.” This is non-trivial by the definition given, and no one would have to kill themselves at all.

If that were said to a population of 2 people, one with a blue dot and one with a red dot, the person with the red dot would kill themself immediately

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

#29
post #28

Earlier quoted context omitted.

Yeah, I was thinking about if the stranger said something like, “not all the dots are blue.” This is non-trivial by the definition given, and no one would have to kill themselves at all.

If that were said to a population of 2 people, one with a blue dot and one with a red dot, the person with the red dot would kill themself immediately

Right, but isn’t the challenge supposed to be to prove that in every case, everyone dies? Not that ‘in at least one case, everyone dies’

If it was the latter, a one person town would always die.

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

#30
post #27

Earlier quoted context omitted.

Yeah, I was thinking about if the stranger said something like, “not all the dots are blue.” This is non-trivial by the definition given, and no one would have to kill themselves at all.

"not all the dots are blue" - in the case where there are n people with n-1 blue dots and 1 red dot, the person with the red dot kills themself, and then everyone else kills themselves because they know that the red dot person killed themself because they did not see any red dots.

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”

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