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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]

#191

Post by zem »

gohrt wrote: post #172

Some of these are poorly worded: * Kleptopia is ambiguous about what gets stolen, and what toplogy the boxes/padlocks must have for the solution. * The "clever" solution to Unwanted Expansion isn't a complete proof, unless you add some complicated reasoning or use the non-clever proof, but if you do that, you don't need the "clever" proof at all. * The Wimbledon puzzle doesn't explain the scoring rules of tennis :(

the clever solution to "unwanted expansion" only uses the fact that addition and multiplication of two positive integers a, b > 1 always gives an answer that is greater than both a and b, therefore if the expansion never terminates and all your variables are 2, the overall result will be infinite. since expansion doesn't change a result, the pre-expansion evaluation should also be infinite; since it is not, the expansion terminates.

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

#192

Post by posterboy »

andrepd wrote: post #178
posterboy wrote: post #171

Earlier quoted context omitted.

I am not angry with a feature of the language. I am angry with the people abusing a bug, for lack of a better word, that makes a simple language overly complicated. I am angry, because I didn't understand the whole comment. In my opinion that is not just my fault. It was, in many ways, terribly written. I think a little meta discussion is beneficial. Seeing that it is a question of logic and we are in a logic puzzle…

>What does it matter? Are you saying there is no other way? Why don't you give it a try yourself, it's not hard. For starters, just try replacing "they" with "F". Lol. It does matter because you are bitching about using they when you don't even say what on earth are we supposed to say instead. Replace they with the name? "If the light is on when Franklin gets to the room, Franklin turns the light off, and Franklin in…

So, my personal ability to rephrase the sentence is attacked, the pretense that there would be no alternatives is kept and my idea is dismissed as petty. That's just as expected.

Note that the above sentence is written in the objective way that I mentioned before. There is no way a third person singular gendered pronoun could creep in there, even if I was talking about you in the third person.

Unless Franklin was a transfinite gender fluid with multiple personalities, the use of they would be wrong there, according to the article you linked.

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

#193

Post by wvrvwwwe »

fenomas wrote: post #185
albinofrenchy wrote: post #128

Earlier quoted context omitted.

I think the puzzle as phrased is slightly incomplete. The stranger must communicate something _new_ each day to make the induction work. For instance, if the number of blues is 25, and the (merciful) stranger says that the number of blues is not prime every day, no one ever has enough information. And in fact, even that doesn't seem to be enough. The non-trivial part must be that at least one person knows more than t…

You are overlooking that all the residents gather together each day. Once a visitor has said something nontrivial, after that the new information each day comes when the residents gather, and discover who did or didn't commit suicide the night before. Also: > For instance, if the number of blues is 25, and the (merciful) stranger says that the number of blues is not prime every day, no one ever has enough information…

> This is not correct. Saying "the number of blues isn't prime" just once would be sufficient to start the process, as would "there is at least one blue", etc. It doesn't matter that it's not new information to any one villager.

Sorry, can you explain this part? If there were 10 blues and 10 reds, and the stranger said "there is at least one blue", why would that result in a suicide in any of the dot-town people?

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

#194

Post by twhb »

raziel414 wrote: post #183
twhb wrote: post #148

I collect riddles like these! Here are a few of them. Numbered Hats A warden places a hat on the head of each of 100 prisoners, each with a random number from 1 to 100. There may be duplicates. Each prisoner can see everybody's hat but their own. Each prisoner then guesses their own number; if any guess correctly, they all go free. The group may not communicate in any way during the trial, but may strategize beforeha…

Can you post the solution to the numbered hats one?

Sure.

Call the sum of all assigned numbers N. No prisoner knows N, but they do know that there are exactly 100 possible last two digits of N, from "00" up to "99". Beforehand, assign a different last digit pair to each prisoner. When the prisoner guesses, he sums everybody else's number, then guesses the number between 1 and 100 that, when added to his partial sum, results in his assigned last two digits.

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

#195

Post by fenomas »

wvrvwwwe wrote: post #193
fenomas wrote: post #185

Earlier quoted context omitted.

You are overlooking that all the residents gather together each day. Once a visitor has said something nontrivial, after that the new information each day comes when the residents gather, and discover who did or didn't commit suicide the night before. Also: > For instance, if the number of blues is 25, and the (merciful) stranger says that the number of blues is not prime every day, no one ever has enough information…

> This is not correct. Saying "the number of blues isn't prime" just once would be sufficient to start the process, as would "there is at least one blue", etc. It doesn't matter that it's not new information to any one villager. Sorry, can you explain this part? If there were 10 blues and 10 reds, and the stranger said "there is at least one blue", why would that result in a suicide in any of the dot-town people?

That's exactly the puzzle!

If you'd like a hint, imagine that there are only two villagers - you're one of them, and the other one has a blue dot. A visitor tells you both "there is at least one blue". You already knew that, but did he? And what happens the following day, when you see him still alive (or don't)?

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

#196

Post by fenomas »

tiglionabbit wrote: post #155
JoeAltmaier wrote: post #149

Earlier quoted context omitted.

The clock is certainly necessary. But for information, I think its as easy as "somebody has blue eyes!" said once. If only one person has blue eyes, they see no one else with blue eyes so kill themselves. If two people have blue eyes, they see the other guy and think "maybe its only him". Next day, that guy is still alive; they now know the only remaining blue-eye is themselves; midnight comes and they both suicide.…

If two people have blue eyes, "Somebody has blue eyes" is not new information, because everyone has already seen that someone has blue eyes.

It's not new information to either person individually. But while both people already knew it, they didn't know that the other one knew it. That's the new information.

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

#197

Post by bzbarsky »

cousin_it wrote: post #188
bzbarsky wrote: post #164

Earlier quoted context omitted.

I'm still not quite following. Is the "perimeter" here the sum of the lengths of projections of the edges, then how is that different from "the sum of its projections"? Anyway if you define "perimeter" that way then for the outer box the "perimeter" is in fact 4 * (a+b+c), where a, b, c are the dimensions of the box. I also agree that for the inner box the "perimeter" is at least 4 * (a'+b'+c'), by the triangle inequ…

Let's say the projections of the inner box's edges onto the X axis have three distinct lengths a,b,c (all positive). Also let's say the distance between the leftmost and rightmost projected vertices is d. The nontrivial fact is that d=a+b+c, and not say a-b+c. That leads to the desired inequality, I think.

Ah, I see. Yes, I agree that given that fact you get the desired inequality.

But this fact is, as you say, nontrivial. It's certainly false for various non-box-like shapes afaict, so there's something special to boxes that needs proving here.

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

#198

Post by thomasahle »

jon_richards wrote: post #118
rntz wrote: post #103

Earlier quoted context omitted.

This is indeed the standard solution. There is also a more difficult version: Every prisoner is required to have the same strategy (so you cannot pick a unique person F). (Every thread runs the same program, and threads do not have access to a unique thread identifier.)

I'll just solve this assuming the light starts off, because otherwise I have a feeling it will get miserable to think through. Every prisoner starts at c=1. If light is on, turn it off and decrement c. If the light is off, turn it on and increment c. It c hits 0, always do nothing. If c=101, everyone has been to the room. Everyone wants to turn off 1 more light than they turn on, but that means one person has to turn…

Very nice solution.

I wonder if it can be made not rely on randomness at all. The 'standard' solution just required that every prisoner would be taken to the room infinitely many times. As long as this was the case, the warden could try any devious sequence they liked.

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

#199

Post by thomasahle »

twhb wrote: post #194
raziel414 wrote: post #183

Earlier quoted context omitted.

Can you post the solution to the numbered hats one?

Sure. Call the sum of all assigned numbers N. No prisoner knows N, but they do know that there are exactly 100 possible last two digits of N, from "00" up to "99". Beforehand, assign a different last digit pair to each prisoner. When the prisoner guesses, he sums everybody else's number, then guesses the number between 1 and 100 that, when added to his partial sum, results in his assigned last two digits.

This makes sense, though twhb didn't mention any restriction on the numbers you might guess. Thus the first prisoner could just guess on the entire sum they saw, and only two guesses would be needed.

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

#200

Post by posterboy »

evanb wrote: post #174
posterboy wrote: post #147

Earlier quoted context omitted.

Good grief. If you want to write objective, do so, and ommit personal pronouns all together, but don't employ this archaic, confusing grammatical quirk. I'd like to point out to you, ekke's comment was much better understandable and shorter. Edit: Did you even read what you linked? > One explanation given for some uses of they referring to a singular antecedent is notional agreement, when the antecedent is seen as se…

Although you allege ekke's comment was "much better understandable", it commits the same use of they as singular. > Others follow a simple pattern - if the light is off, and they have never turned it on yet, turn it on. If it is already on, or they have already ever turned it on, do nothing. "They" cannot possibly be referring to the group---"they" is referring to each person individually. If it's referring to the ot…

"Others" is not singular. "they" is a reference to individuals out of a group. "they each" is a common disambiguation, but it doesn't actually matter who turns the light on. The generic he was also used, anyway. This "they" is commonly used to refer to groups of only males, too, and has nothing to do with gendering.

In contrast, F was really singular.

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