Pick a number between 1 and 10

[Fred Nerd]

I have no idea if anyone else has done this before but I decided to answer this once and for all.

You know where Marvin the Paranoid Android is demonstrating his intelligence to the mattress and asks it to pick a number between 1 and 10, and the matress says (IIRC) 7 and Marvin crushingly points out that it's wrong and how stupid the mattress is?  Well I thought I'd work it out.

The answer is 2

And I'll hide the reasoning so that others have a chance to think about it and tell my why I'm wrong and why they they are smarter than Marvin.

Spoiler (click to show/hide)

First we have to work out some rules. The fact that a robot asks it would mean it's safe to presume there is a correct answer.
Also, it's important to note that it's NOT 1 and 10 INCLUSIVE
Now, the only way there can be a correct answer is if there is only one number between 1 and 10. Which means that the question must be in a context that only allows this. The simplest context is if it is in base 3 (trinary) so the counting numbers would be 0,1,2,10,11,12,20, etc
In this case, the answer is 2.
Very simple.

[MilesAhead]

I don't understand the reasoning bit.  But do you know the riddle about 2 guards to a treasure(like an Indiana Jones riddle) .. one guard has to always answer truthfully.  The other guard must always answer with a lie.  You have one question to determine which is which.  What is the question and which guard do you ask?

Edit:  I don't remember the solution.  That's why I'm asking.

[Stoic Joker]

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

[MilesAhead]

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

Ok, now I get it.  I remembered the part about asking what the other would say.  But the logic escaped me.  Thanks. 

[MilesAhead]

@Fred.  I get it now.  I didn't grok the base 3 part the first time I read it. 

[SeraphimLabs]

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

Its easier to just kick them in the shin and ask if it hurt. Then you know which one is telling the truth and which one isn't.

Of course your solution is less likely to piss them off.

[MilesAhead]

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

Its easier to just kick them in the shin and ask if it hurt. Then you know which one is telling the truth and which one isn't.

Of course your solution is less likely to piss them off.

Plus assuming they are guarding something of great value implies they have weapons at the ready to prevent entry and/or dispatch intruders.  But now that you mention it, a simpler solution might be asking either "If I try to kick you in the nuts will you kill me?"  If the guard answers "no" he's the liar.

[Renegade]

That's a stupid bait & switch question. The logic just doesn't follow. If you go down that path you end up admitting any base system, which is idiotic. What happens when some smartass comes up with base 0.2 or something similarly silly?

Mensa problems often suffer from the same issues -- they phrase a problem for which there are several answers/solutions, then pull the rug out from under you and yell, "Oh, that's not what we meant! We meant something entirely different!" Smart people are often idiots.

This is a general problem and is best articulated by Zeno of Elea around 2500 years ago. What system are you working in? It matters.

[MilesAhead]

Mensa problems

This makes me think of a Columbo episode where the murderer bumps off a fellow member of a genius society.  He gives Columbo a riddle to solve.  I can't remember the details.  But it has something to do with a bunch of gold ingots, one of which is fake.  There is a scale that gives a printed readout.  IOW a card with the weight so you cannot do stuff like stand on it and have somebody hand you an ingot at a time.  You get to make 2 measurements to determine which is the fake ingot.

Something like that.  It's pretty nebulous to search on all that. I haven't been able to get the language of the riddle.

But to your point Ren, I always felt in Chemistry class in high school that there were "observations" inserted into the exams so that only a coached candidate could get 100%.  I mean some of the cockamamie things "observed" were such that no normal person would think of them.  You had to read the prep notes to know what to answer or you would miss 2 or 3 on every question.

Edit:  I found the Mensa Riddle and Solution

[SeraphimLabs]

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

Its easier to just kick them in the shin and ask if it hurt. Then you know which one is telling the truth and which one isn't.

Of course your solution is less likely to piss them off.

Plus assuming they are guarding something of great value implies they have weapons at the ready to prevent entry and/or dispatch intruders.  But now that you mention it, a simpler solution might be asking either "If I try to kick you in the nuts will you kill me?"  If the guard answers "no" he's the liar.

Not necessarially. For that to be reliable you would have to know in advance how the guards would respond to your provocation. Some guards would chop off your head right away, others would simply remain at their posts and shrug it off.

Actually kicking them gives you an undisputed fact from which you can judge their responses.

Working along these lines a little more, it would really work with any well known or easily observed fact. Kicking them with its associated risk of death is not required.

Also relevant: http://xkcd.com/246/

[Stoic Joker]

A key part of the bit is that you're only allowed to ask one question.

[mouser]

Far be it from me to inject a real question into this thread, but here is a real question:
In our normal base 10, we have a protocol for SPEAKING large numbers, so 154 is "one hundred and fifty four".
Using the same logic, what would be the generic method for similarly SPEAKING large numbers in other bases?

[MilesAhead]

Not necessarially. For that to be reliable you would have to know in advance how the guards would respond to your provocation

Since the setup is an Indiana Jones type scenario I think it's safe to assume any attempt to attack a guard would be met with lethal force.  The attack would be interpreted as an attempt to pass without solving the riddle.

[MilesAhead]

Far be it from me to inject a real question into this thread, but here is a real question:
In our normal base 10, we have a protocol for SPEAKING large numbers, so 154 is "one hundred and fifty four".
Using the same logic, what would be the generic method for similarly SPEAKING large numbers in other bases?

My guess would be that decimal based would be considered the default.  Therefore if one sees 0xFF on the page and says "two hundred and fifty five," one would be correct.  Speaking a number in another base would require specifying the base as in "FF Hex" or "three seven seven octal."  But perhaps the math experts here know for certain.

[Stoic Joker]

In our normal base 10, we have a protocol for SPEAKING large numbers, so 154 is "one hundred and fifty four".

IIRC you aren't supposed to say and when speaking numbers...did that change?

[mouser]

My guess would be that decimal based would be considered the default.  Therefore if one sees 0xFF on the page and says "two hundred and fifty five," one would be correct.

Well I was really asking if there was a logical way to speak such numbers WITHOUT converting them first to base 10 and speaking in base 10.

[MilesAhead]

My guess would be that decimal based would be considered the default.  Therefore if one sees 0xFF on the page and says "two hundred and fifty five," one would be correct.

Well I was really asking if there was a logical way to speak such numbers WITHOUT converting them first to base 10 and speaking in base 10.

I'm self taught so I'm not sure of the conventions.  But my assumption would be anything spoken without the base specifier would be assumed to be decimal.  So if the written number was 0x0F I would either say "F Hex" or "fifteen."

I guess if it was a long decimal base number and I didn't want to take the time to figure out what it was, like 103023345665432445 I would just read out the digits and the listener would assume it was decimal unless specified otherwise.

[Deozaan]

Far be it from me to inject a real question into this thread, but here is a real question:
In our normal base 10, we have a protocol for SPEAKING large numbers, so 154 is "one hundred and fifty four".
Using the same logic, what would be the generic method for similarly SPEAKING large numbers in other bases?

IMO writing and speaking are two different things. Words don't mean anything, except the meaning we give them. Spoken words are sounds that represent ideas. Written words are symbols to represent ideas. Neither spoken nor written language has any inherent meaning. Otherwise we wouldn't have to learn how to speak/write other languages. "15" does not mean "fifteen" just as it doesn't mean "0x0F". However, from a mathematical point of view, when talking about the numbers these symbols/sounds represent, 15 is equal to fifteen is equal to 0x0F. Therefore they can be used interchangeably. Since (to the best of my knowledge) nearly all humans use base-10 when speaking numbers, it would be correct to pronounce 0x0F as the base-10 equivalent (15) in the language you are speaking.

It's all just a different way to say the same thing. We encounter the same issue in spoken languages as well. I might say "fifteen" but someone who doesn't speak English will have no idea what I'm talking about. Or even if someone does understand English, but the rest of the conversation is happening in French, someone would be understandable confused if I suddenly said "fifteen" using a different language.

In other words, use the language you will be understood in, as determined by context and requirements (obviously you should say/write 0x0F if you're talking about a computer data type that must be in hex) of the overall conversation.

Of course, part of the point of a riddle is to be tricky. And saying "ten" when you're talking about "10" in binary is intentionally misleading, not to mention technically incorrect. That's why it works better as a written riddle/pun. Because you're not giving yourself away that you really mean "two", e.g.,:

There are 10 kinds of people in this world: Those who understand binary, and those who don't.

[tomos]

You could do something like the imperial monetary system (£sd) that we had till 1970.
It starts with a penny (1d)
then you have a thrupenny bit,
then a 6 penny bit, then:
12 pence = 1 shilling
20 shillings = 1 pound (£1) = 240d (i.e. pence)

To complicate things further, there was:
four farthings or two hapennies to a penny,
a twobob (2 shilling) coin (=24 pence - but also 1 tenth of a pound (!)),
and two-shillings & six-pence (2.5 shillings = 30 pence) as a half-crown coin (even though the crown coin no longer existed)

Not sure what base that all is though

[x16wda]

Not sure what base that all is though

Base villain.

[Fred Nerd]

There are 10 kinds of people in the world, those who understand binary, those who don't, and those who know trinary.

@renegade I challenge you to find another base system which has the series 1,  [another number] and 10.

As for how they're spoken, I don't know.
Although I would imagine Octal is spoken like the decimal it looks like  e.g. 27oct would be Twenty-Seven, octal.

Hex is annoying because it can't be spoken in a lot of cases so it has to be spelled out.

Decimal is annoying because people keep saying things like 'a couple' 'a dozen' 'a grand'
Not to mention plumber's numbers where $150 turns out to be really $375.

[Renegade]

I forget where, but I have seen some proposals for speaking non-base 10 numbers. However, part of the point of language is to communicate, and secret languages for which only a few initiates exist do not really serve well for general communication.

The most common non-base 10 system in use is base 60, which is used to tell time. When speaking "11:00" we still stay "eleven o'clock", the same as in base 10.

While "10" could be construed as ambiguous for "two" or "eight" or "ten" or "sixteen", etc., it's disingenuous to assume anything other than base 10 in normal situations. There are only a few places where we might wonder, but those situations are almost always explicitly clear, e.g. 0x10 indicates that we're using base 16, and when they are not, they are made clear.

Relevant: http://en.wikipedia.org/wiki/Wordplay_(The_Twilight_Zone)

https://www.youtube.com/watch?v=iT7JgH3VGfU

Also...

http://www.gutenberg.org/files/12/12-h/12-h.htm  

'And only ONE for birthday presents, you know. There's glory for you!'

'I don't know what you mean by "glory,"' Alice said.

Humpty Dumpty smiled contemptuously. 'Of course you don't—till I tell you. I meant "there's a nice knock-down argument for you!"'

'But "glory" doesn't mean "a nice knock-down argument,"' Alice objected.

'When I use a word,' Humpty Dumpty said in rather a scornful tone, 'it means just what I choose it to mean—neither more nor less.'

'The question is,' said Alice, 'whether you CAN make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be master—that's all.'

Alice was too much puzzled to say anything, so after a minute Humpty Dumpty began again. 'They've a temper, some of them—particularly verbs, they're the proudest—adjectives you can do anything with, but not verbs—however, I can manage the whole lot of them! Impenetrability! That's what I say!'

'Would you tell me, please,' said Alice 'what that means?'

'Now you talk like a reasonable child,' said Humpty Dumpty, looking very much pleased. 'I meant by "impenetrability" that we've had enough of that subject, and it would be just as well if you'd mention what you mean to do next, as I suppose you don't mean to stop here all the rest of your life.'

'That's a great deal to make one word mean,' Alice said in a thoughtful tone.

[Renegade]

There are 10 kinds of people in the world, those who understand binary, those who don't, and those who know trinary.

@renegade I challenge you to find another base system which has the series 1,  [another number] and 10.

Good joke, and good example!

There are no other systems that fit there. That's only trinary.

0, 1, 2, 3, 4, 5, 6, 7, 10...

As there the only possible base is octal.

As for how they're spoken, I don't know.
Although I would imagine Octal is spoken like the decimal it looks like  e.g. 27oct would be Twenty-Seven, octal.

I don't use octal much at all, and probably only a handful of times over the years. But any base less than 10 could use that convention. It would seem odd though saying binary 100 as "one hundred". With binary we're accustomed to still saying the number as it is instead of "reading" it, i.e. "four" in that case. But, I think binary is pretty commonly used and understood, comparatively.

Hex is annoying because it can't be spoken in a lot of cases so it has to be spelled out.

That's how I say hex -- just reading out digits.

Not to mention plumber's numbers where $150 turns out to be really $375.

Hahaha!

In some circles, they quite literally say "plus alpha".

[MilesAhead]

Not to mention plumber's numbers where $150 turns out to be really $375

And air conditioner air filters that aren't the specified size.  You have to know the fudge factor when buying them, especially online.