1762: "Moving Boxes"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Tue Nov 22, 2016 11:49 am UTC

I've had cause to think of my house contents recently. By weight, I think most of my boxes would just be labelled "Books". Bookshelves would be the dominant furniture type (but are themselves necessarily much lighter, and doesn't count the 'bookcase' that is the floor).

(And having thought I'd just mentally counted all the bookcases in my house, I've just realised that there are two more, just a small head turn away, that I'd totally forgotten.)

User avatar
addams
Posts: 10332
Joined: Sun Sep 12, 2010 4:44 am UTC
Location: Oregon Coast: 97444

Re: 1762: "Moving Boxes"

Postby addams » Tue Nov 22, 2016 2:10 pm UTC

Flumble wrote:
addams wrote:uh-oh....Is someone moving?
xkcd: Soon to be coming from Canada?

Given his express interest in the Netherlands in the past, maybe xkcd will be dutch soon? :mrgreen:

..oh...Right. Good on him.
..Yes. That would be my first choice, too.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

ps.02
Posts: 378
Joined: Fri Apr 05, 2013 8:02 pm UTC

Re: 1762: "Moving Boxes"

Postby ps.02 » Tue Nov 22, 2016 5:05 pm UTC

orthogon wrote:
ps.02 wrote: [...] CLOCKS (FAST) [...]

If you mean that the clocks gain time, a good GR-aware removal company will put them in the attic of the new house. (Or is it the basement?)

Attic, I think. It's really easy to confuse which direction the effect goes, for you and me both.

(Note though: maximum gravity isn't the basement, but ground level - it goes to zero as you approach the center of the earth. So, do put CLOCKS (SLOW) in the basement, but only in the expectation that they can be hung high on the walls.)

ShifterCat
Posts: 16
Joined: Sun Jul 11, 2010 3:43 am UTC

Re: 1762: "Moving Boxes"

Postby ShifterCat » Tue Nov 22, 2016 7:12 pm UTC

azule wrote:Is a box labeled Pornography more or less likely to be "mishandled" by paid movers?


Well, apparently the ruse worked, so I guess the movers were either too embarrassed or too scared to look.

User avatar
Wee Red Bird
Posts: 193
Joined: Wed Apr 24, 2013 11:50 am UTC
Location: In a tree

Re: 1762: "Moving Boxes"

Postby Wee Red Bird » Wed Nov 23, 2016 8:25 am UTC

In my last move, I had a box marked The decapitated heads of my enemies Garage Stuff. Was left in the middle of the garage.

PKM
Posts: 7
Joined: Tue Sep 08, 2015 9:57 am UTC

Re: 1762: "Moving Boxes"

Postby PKM » Wed Nov 23, 2016 11:48 am UTC

Perhaps I've been watching too much Only Connect: my instinct on seeing an image like this is that there's some cryptic pattern to the box labels, usually involving the letters in the words and not the words themselves. Words ending with A-M on the left, N-Z on the right, or the number of unique vowels increases as you go down levels (so garam masala goes on the top and sequoia seeds on the bottom) and I have to figure out the pattern for 5 marks on my non-verbal reasoning exam.

Is there any such pattern discernible here or are the labels just fanciful box contents?

Also I agree that the box labeled
"DARK
MATTER"
contains both dark and matter - the only other obvious multi-word phrase is "field lines" and that appears on a single line.

Plutarch
Posts: 103
Joined: Fri Apr 17, 2009 10:29 am UTC
Location: London, UK

Re: 1762: "Moving Boxes"

Postby Plutarch » Wed Nov 23, 2016 1:17 pm UTC

I've moved houses quite often. I've never labelled a box. Is it a normal thing to do? Do most people do it?

rmsgrey
Posts: 3655
Joined: Wed Nov 16, 2011 6:35 pm UTC

Re: 1762: "Moving Boxes"

Postby rmsgrey » Wed Nov 23, 2016 3:10 pm UTC

Plutarch wrote:I've moved houses quite often. I've never labelled a box. Is it a normal thing to do? Do most people do it?


Last time we moved, we used boxes labelled using an Xnn schema - X being a prefix indicating which room (or at least region) of the house to move it to; nn being a number. We also had inventory sheets summarising the contents of each numbered box.

So the removal men could be told "boxes starting with K go in the Kitchen; anything starting D can stay downstairs; anything else goes upstairs" or similar.

User avatar
azule
Saved
Posts: 2132
Joined: Mon Jul 26, 2010 9:45 pm UTC
Location: The land of the Golden Puppies and Rainbows

Re: 1762: "Moving Boxes"

Postby azule » Wed Nov 23, 2016 8:09 pm UTC

Plutarch wrote:I've moved houses quite often. I've never labelled a box. Is it a normal thing to do? Do most people do it?

I used to label them. But, eh, don't anymore. If you don't label them it's like Xmas morning everyday until you're done unpacking. ;)
Image

If you read this sig, post about one arbitrary thing you did today.

I celebrate up to six arbitrary things before breakfast.
Time does drag on and on and contain spoilers. Be aware of memes.

User avatar
ucim
Posts: 6890
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: 1762: "Moving Boxes"

Postby ucim » Wed Nov 23, 2016 10:32 pm UTC

I think I used to label them, but it's been too long. However, some time ago I got a two line phone that iets me forward an incoming call on one line to a different number via a different line. It's a really cool feature and is the main reason I got the phone. As it turns out, the one time it would have come in handy, I didn't set it up, and missed a very important call (about a house I was negotiating over). Ironically, I was actually just upstairs, in the real estate office of my landlord and agent (who wasn't the one making the call though).

Anyway, we got the house, I packed the phone in with all my other stuff in boxes that were probably labeled well enough (it would have been my style), and we moved in. It's been over thirty years and the phone has not turned up. In fairness, not all boxes got opened either, perhaps because of what the labels said. And actually, I don't even know where the unopened boxes are at this point.

As an aside, I got some cheap padlocks for free. They are of the type that has ten buttons, and you depress five of them (they stay depressed; the order doesn't matter) and you can open the lock. I wrote the combination on the lock in magic marker, but in a non-obvious but easy to remember code.

I have no idea what the code is anymore, can't figure out the combination, and can't open the lock. I guess the code was good enough. :)

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Wed Nov 23, 2016 11:47 pm UTC

ucim wrote:As an aside, I got some cheap padlocks for free. They are of the type that has ten buttons, and you depress five of them (they stay depressed; the order doesn't matter) and you can open the lock. I wrote the combination on the lock in magic marker, but in a non-obvious but easy to remember code.

I have no idea what the code is anymore, can't figure out the combination, and can't open the lock. I guess the code was good enough. :)

Just 252 combinations, easily permuted through, if I've worked it out correctly... Give it a go, and you'll probably get the first open within twenty minutes, the second within ten (having got into the pattern, through the practice on the first), and the rest in not much over five, if even that. Especially if you find yourself able to back-calculate your clue-code.

Quicker, if its the old type that has a subtle 'feel' when you spoil the code. (Like the early door locks with 1..9,0,X,Y,Z and the C for the reset (was that maybe 6 of 13 keys pressed, for 1716 combos?) , like I remembered playing with back in the '80s each time we visited a campsite with one of those on the pedestrian access gate/door-in-the-boundary-wall. Having the current code, on each visit, but also having plenty of time on my hand... ;) )

User avatar
ucim
Posts: 6890
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: 1762: "Moving Boxes"

Postby ucim » Thu Nov 24, 2016 3:34 am UTC

Soupspoon wrote:Just 252 combinations, easily permuted through, if I've worked it out correctly... Give it a go, and you'll probably get the first open within twenty minutes...
Yeah, not worth it. They were really junk locks anyway and I don't even know if I have them any more.

There was another I lost the combination to - it was one of those brass ones with four dials numbered 0-9, so 10000 combinations. You had to push the hasp in to get it to spring out, and you could change the combination. 0000 push 0001 push 0002 push.... I got halfway through before giving up. Took forever. Even odds I passed the combination and it didn't open because, well, sometimes they stick. Dunno where that one is either.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

User avatar
Sableagle
Ormurinn's Alt
Posts: 2151
Joined: Sat Jun 13, 2015 4:26 pm UTC
Location: The wrong side of the mirror
Contact:

Re: 1762: "Moving Boxes"

Postby Sableagle » Sun Nov 27, 2016 1:37 am UTC

Most "cheap and crappy little" locks can be opened with 55645 and a few symbols.
Zohar wrote:You don't know what you're talking about. Please spare me your quote sniping and general obliviousness.

CorruptUser wrote:Just admit that you were wrong ... and your entire life, cyberspace and meatspace both, would be orders of magnitude more enjoyable for you and others around you.

User avatar
ucim
Posts: 6890
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: 1762: "Moving Boxes"

Postby ucim » Sun Nov 27, 2016 4:46 am UTC

Sableagle wrote:Most "cheap and crappy little" locks can be opened with 55645 and a few symbols.

It can probably be opened with a screwdriver. The buttons are all plastic.

However, the combination is not 55645. There are ten buttons, and each one is either pushed or not pushed. Exactly five are pushed. 12467 is a possible combination, but 12255 (equivalent to 125) is not. I don't even know if I have them, but if I do, I'll post the code and see if any of you can figure it out.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

User avatar
Sableagle
Ormurinn's Alt
Posts: 2151
Joined: Sat Jun 13, 2015 4:26 pm UTC
Location: The wrong side of the mirror
Contact:

Re: 1762: "Moving Boxes"

Postby Sableagle » Sun Nov 27, 2016 8:09 am UTC

The symbols are a decimal point, a multiplication sign and a couple of lower-case "m"s. Get the angle right and have a bucket of water there.
Zohar wrote:You don't know what you're talking about. Please spare me your quote sniping and general obliviousness.

CorruptUser wrote:Just admit that you were wrong ... and your entire life, cyberspace and meatspace both, would be orders of magnitude more enjoyable for you and others around you.

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Sun Nov 27, 2016 5:34 pm UTC

ucim wrote:
Sableagle wrote:Most "cheap and crappy little" locks can be opened with 55645 and a few symbols.

It can probably be opened with a screwdriver. The buttons are all plastic.

However, the combination is not 55645. There are ten buttons, and each one is either pushed or not pushed. Exactly five are pushed. 12467 is a possible combination, but 12255 (equivalent to 125) is not. I don't even know if I have them, but if I do, I'll post the code and see if any of you can figure it out.

Jose

You're thinking of the combinations wrongly.
They range from 0000011111 to 1111100000, 'binary' pressed/not pressed by each 1 or 0, but the transition is the next 'binary' number of exactly five set (and five unset) bits.
One transition is:
0000011111
0000101111 (most significant bit shifted)
0000110111 (each next-most
0000111011 significant bit now
0000111101 shifted into the
0000111110 gap opened up)
0001001111 (shift the MSB again)
0001010111 (move the nMSB into the gap)
0001011011 (into whose own
0001011101 gap you shuffle
0001011110 the remainder)
0001100111 (then reset tyem aw you move the nMSB [ifurther][/i] into the gap)
... Repeat with the dregs to get the nextnMSB to the gap ceiling of the doublegap, then the nnnMSB, until the entire gap is atbthe bottom, then reset the (n+)MSBs whilst moving the MSB up to create a triple-gap, which you then shuffle into with similar methods.
(This order just handily follows the subset of all binary numbers that fulfil the 'five set bits' rule, there are better transitions that work like a bidirectional bubble-sort that would minimise switch-flicking in a 'permute until it works' way, but as you probably have to press an eleventh 'reset' button after each failed attempt, that's reset+five+try on each attempt after the initial one, regardless, so a good sequence that you can keep track of probably is best.)

That's the 'physical layer' model, but you can also look at the sequences, in abstraction, as a(n inferior) form of Run-Length Encoding. The number of 0s between each 1, or if you prefer) the number of 1s between each zero. Taking the latter (counting the trailing digits-of-note as counted until the end-of-sequence with the above pattern, you have 00005, 00014, 00023, 00032, 00041, 00050 then 00104, 00113, 00122, etc, which (with less digits than ten) you again get a consistent an ascending list of numbers in an arbitrary base that is actually also limited to a sum-of-all-digits being exactly five.

...and I want to go onto how you can find the number of combinations through that variably-variable-base counting system, but I'm about to sit down to a meal with relatives, and I'll be getting funny looks if Imdon't engage with their conversation. I'll leave it there, and maybe come back to it later...

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Sun Nov 27, 2016 10:39 pm UTC

...tell you what, I won't go into the number of combinations, because that rushed (typo-laden) message probably belongs more in the Mathematics forum.

But I'll start you off, if you want to work it out yourself. The full (0|1)x10 space is of course 210 combinations. But you can remove the single combination that is 0000000000 and the opposite one that is 1111111111, obviously. And the ten from 0111111111 to 1111111110 with a single zero taking each position, ditto all-but-one-are-zero with a travelling 1. And for two not-like-the-rest, it gets complicated but calculable (hint: 1-and-one-in-nine plus 0-and-2-in-nine, the latter of which is 1-and-one-in-eight plus..., etc), which leads you on to the (two complimentary) three-unlike-the-rest and onward yet until four-unlike-the rest, all paired. Subtract those totals from the 210, as what is left is five-and-five total.

(Four-and-six was easier for me to work out, through reduction, than the five-and-five, so going the long way round, later confirmed with brute force, was my method. But maybe there's a better direct method, after all, based upon a single recursive value.)

User avatar
Sableagle
Ormurinn's Alt
Posts: 2151
Joined: Sat Jun 13, 2015 4:26 pm UTC
Location: The wrong side of the mirror
Contact:

Re: 1762: "Moving Boxes"

Postby Sableagle » Sun Nov 27, 2016 10:47 pm UTC

While you were working that out I walked to the hardware store, bought a pair of bolt croppers, walked back and cut the lock off. :P
Zohar wrote:You don't know what you're talking about. Please spare me your quote sniping and general obliviousness.

CorruptUser wrote:Just admit that you were wrong ... and your entire life, cyberspace and meatspace both, would be orders of magnitude more enjoyable for you and others around you.

User avatar
ucim
Posts: 6890
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: 1762: "Moving Boxes"

Postby ucim » Sun Nov 27, 2016 11:32 pm UTC

The number of combinations is just ten choose five. That is, 10! / (5!*5!) which equals 10*9*8*7*6 / (5*4*3*2)

This equals (2*9*2*7*2) / 2 which is 7*9*4 = 252

Soupspoon wrote:One transition is:
0000011111
0000101111 (most significant bit shifted)
0000110111 (each next-most
That's actually the basis of my code. Each lock had some letters on it. Consider a lock that had "ADE" written on it.

Sableagle wrote:While you were working that out I walked to the hardware store, bought a pair of bolt croppers, walked back and cut the lock off. :P
While you were at the store, I used a bic pen to poke the plastic buttons out (each of them actually goes completely through the lock).

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

User avatar
Flumble
Yes Man
Posts: 2264
Joined: Sun Aug 05, 2012 9:35 pm UTC

Re: 1762: "Moving Boxes"

Postby Flumble » Sun Nov 27, 2016 11:38 pm UTC

You were all talking past each other.
I was really confused about the conversation between Soupspoon, ucim and Sableagle until I realized that.

Sableagle wrote:Most "cheap and crappy little" locks can be opened with 55645 and a few symbols.

Apart from ucim's locks being either 10 buttons or a 4-digit combination, so it's not a response to ucim, I have no clue what kind of lock can open with '55645 and a few symbols'.

@Soupspoon, since the whole space of 2^10 is only 4 times as large, just trying all binary codes is less error-prone and might be just as fast if you're familiar with binary adders (or snakes). Then again, if you have to reset the buttons after every try, it's faster and less error-prone to write a script that shows you visually which buttons to press for every try.


ucim wrote:Consider a lock that had "ADE" written on it.

I'd rather do a known-plaintext attack. :mrgreen:

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Mon Nov 28, 2016 12:14 am UTC

ucim wrote:The number of combinations is just ten choose five. That is, 10! / (5!*5!) which equals 10*9*8*7*6 / (5*4*3*2)

This equals (2*9*2*7*2) / 2 which is 7*9*4 = 252

I gotta think through that "m choose n == m!/(n!²)" thang, there. Doesn't sound right, to me, but you got the right result anyway. (I departed from the statistical mathematics route at the Further Education level, so even though I've worked alongside statisticians later on I'm perhaps lacking some of the standard non-self-derived formulae and understandings.)

Anyway, at "10*9*8*7*6 / (5*4*3*2)" I'd go further than you to reduce that by (10/5=2), (8/4=2), (9/3=3) and (6/2=3) to become "2*3*2*7*3" over unity, to the same result.

Consider a lock that had "ADE" written on it.
Well straight hex is no good, 1010 1101 1110 has overflow (whichever way) on ten bits, assuming no deliberate 'junk bits' (and it's 8v4, not 7v5 with the 5 being important). Even with bigendian/littleendian switching at either bit or demi-byte level, it doesn't. And you reply to the binary depictions, not the RLEish ones, so it aintn't based upon that, even if ADE = 1,4,5. (1,5,4 could be 1000001111, but that means another layer of code transposition.) Maybe you're encoding initial parity? But in a(n unsolved) sample of one there's really too few clues. If you'd care to expand the sample in either dimension (or ideally both..?) then maybe we could do better than those people you had originally intended the locks to intellectually defeat... If we could do it with one such example, any half-determined couriering professional with multiple examples (and/or a plastic pen!) could surely have cracked your code (if not locks!).... ;)

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Mon Nov 28, 2016 12:50 am UTC

Reply to self, deliberately, to record my thoughts on the matter...

Soupspoon wrote:
ucim wrote:The number of combinations is just ten choose five. That is, 10! / (5!*5!) which equals 10*9*8*7*6 / (5*4*3*2)

This equals (2*9*2*7*2) / 2 which is 7*9*4 = 252

I gotta think through that "m choose n == m!/(n!²)" thang, there. Doesn't sound right, to me, but you got the right result anyway.

I set about thinking it through and soon realised that it wasn't "m!/(n!²)", it was "m!/(n! * (m-n)!)"... n! being all possible combinations of (for any given five bits) you can select those bits to mark as (say) 1. And the (m-n)! being all possible combinations of selecting the (other!) bits and marking them as (say) 0. (It just happens that m-n=n, of course.)

And then it took a few more minutes (more than it should have) to realise that the m! is therefore all the possible orders to choose "set a first 1 (of ten), second 1 (of nine), third 1 (of eight), fourth 1 (of seven), fifth 1 (of six), first 0 (of five), ... fifth 0 (of one)". The 10! and the 5! approaches I had considered myself in working out the original combination number, the other day, then excluded because of needing to irreleventise the order. But with all orders of 1111100000 above the divisor line and then (all orders of 11111) and (all orders of 00000) below the line, naturally it cancels out the unwanted ordering multiplicities in each case and gives us the orderless result.

I liked doing that. It is just past midnight, local time, and already I have just learnt a completely new thing, today. Thank you.

User avatar
Sableagle
Ormurinn's Alt
Posts: 2151
Joined: Sat Jun 13, 2015 4:26 pm UTC
Location: The wrong side of the mirror
Contact:

Re: 1762: "Moving Boxes"

Postby Sableagle » Mon Nov 28, 2016 4:44 pm UTC

Yep. That bit I remember: mCn = m! / n! (m-n)! and mPn = m! / (m-n)!, numbers of combinations and permutations of n from m.

5.56x45mm versus good locks.
Zohar wrote:You don't know what you're talking about. Please spare me your quote sniping and general obliviousness.

CorruptUser wrote:Just admit that you were wrong ... and your entire life, cyberspace and meatspace both, would be orders of magnitude more enjoyable for you and others around you.

User avatar
orthogon
Posts: 3103
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1762: "Moving Boxes"

Postby orthogon » Mon Nov 28, 2016 5:59 pm UTC

The whole m!/(m-n)! thing always bothered me, since it's just a notational trick for writing "the product of the integers between (m-n+1) and n" (actually you could use big-pi notation, which would be better). It's not as though calculating the factorials and dividing them is more efficient than calculating the product you actually need, and it obfuscates the derivation (pick one of n, then for the next choice you've got n-1 to choose from, etc; repeat m times), which you can easily do in your head.
xtifr wrote:... and orthogon merely sounds undecided.

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: 1762: "Moving Boxes"

Postby Soupspoon » Mon Nov 28, 2016 6:18 pm UTC

It is handier to notate, though, than doing a sum (for n-m+1 to m) of ln(x) and then raising that back up as a power of e, or somesuch alternate workaround. ;)

User avatar
Sableagle
Ormurinn's Alt
Posts: 2151
Joined: Sat Jun 13, 2015 4:26 pm UTC
Location: The wrong side of the mirror
Contact:

Re: 1762: "Moving Boxes"

Postby Sableagle » Mon Nov 28, 2016 7:16 pm UTC

orthogon wrote:The whole m!/(m-n)! thing always bothered me, since it's just a notational trick for writing "the product of the integers between (m-n+1) and n" (actually you could use big-pi notation, which would be better). It's not as though calculating the factorials and dividing them is more efficient than calculating the product you actually need, and it obfuscates the derivation (pick one of n, then for the next choice you've got n-1 to choose from, etc; repeat m times), which you can easily do in your head.

That's what I lined up in my head to make sure I had it right before I clicked "Submit," yes. With a calculator, the ! button is the way to go. Without it, doing only 11+ stuff, cancelling out the numbers first is the way forward.

Number of possible combinations of 6 balls from the 59 now used in our National Lottery:

59*58*57*56*55*54*53*52*51*...*2*1
53*52*52*...*2*1 * 6*5*4*3*2*1

59*58*57*56*55*54
6*5*4*3*2*1

59*5829*57*5614*5511*543
61*51*41*31*21*1

45057474

Forty-five million to one against you hitting the jackpot, and even if you do you have to share it, with probability 1 - (1 - 1/45057474)"15 to 45 million". 71.68% probability that nobody else hits it, assuming no bias in number selection among other players. Non-zero probability that 132 other people hit the jackpot, as apparently happened back in '95. They got £122,510 each.

That would be almost enough to buy a 3-bedroom end-terrace here, so it's totally relevant to moving boxes.
Zohar wrote:You don't know what you're talking about. Please spare me your quote sniping and general obliviousness.

CorruptUser wrote:Just admit that you were wrong ... and your entire life, cyberspace and meatspace both, would be orders of magnitude more enjoyable for you and others around you.

User avatar
ucim
Posts: 6890
Joined: Fri Sep 28, 2012 3:23 pm UTC
Location: The One True Thread

Re: 1762: "Moving Boxes"

Postby ucim » Mon Nov 28, 2016 10:02 pm UTC

orthogon wrote:The whole m!/(m-n)! thing always bothered me, since it's just a notational trick...
Well, pretty much all notation is a trick. m*n is just a tricky way of writing m+m+m+m+m+m+m+ (n times). I'd propose overloading the factorial operator to make it binary:

m!n would be m*(m-1)*(m-2)...*(n+2)*(n+1)*n. Thus m! would be a shorthand ("trick") for m!1, m!m would equal m, and m!n would only be defined for positive integers where m>=n (although the definition could be expanded to make m!n=n!m since multiplication itself is commutative).

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

Tyndmyr
Posts: 11443
Joined: Wed Jul 25, 2012 8:38 pm UTC

Re: 1762: "Moving Boxes"

Postby Tyndmyr » Mon Nov 28, 2016 10:14 pm UTC

Sableagle wrote:Most "cheap and crappy little" locks can be opened with 55645 and a few symbols.


I find they can all be opened rapidly with a dremel. Far more rapid than the above math.

User avatar
Flumble
Yes Man
Posts: 2264
Joined: Sun Aug 05, 2012 9:35 pm UTC

Re: 1762: "Moving Boxes"

Postby Flumble » Mon Nov 28, 2016 11:10 pm UTC

orthogon wrote:The whole m!/(m-n)! thing always bothered me, since it's just a notational trick for writing "the product of the integers between (m-n+1) and n" (actually you could use big-pi notation, which would be better).

...or is it? You can also derive it as: get all the permutations of m items, then, because we only care about the first n items picked, we don't care about the order of the m-n other items so we divide by (m-n)!. Likewise, if you also don't care about the order of the first n items, you divide by n!.
The "choose one of m, choose one of m-1, ..., choose one of m-n" approach is more 'constructive', whereas the "put all m items in all orders, discard all permutations of m-n items" is easier to generalize.

User avatar
da Doctah
Posts: 996
Joined: Fri Feb 03, 2012 6:27 am UTC

Re: 1762: "Moving Boxes"

Postby da Doctah » Tue Nov 29, 2016 1:41 am UTC

The representation using a ratio of factorials is nice as far as definitions go, but fortunately they came up with the specialized notations like C with superscript n and subscript k, or the stacked n and k inside a long pair of parentheses, for convenience in further use.

User avatar
orthogon
Posts: 3103
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1762: "Moving Boxes"

Postby orthogon » Tue Nov 29, 2016 10:30 am UTC

Flumble wrote:
orthogon wrote:The whole m!/(m-n)! thing always bothered me, since it's just a notational trick for writing "the product of the integers between (m-n+1) and n" (actually you could use big-pi notation, which would be better).

...or is it? You can also derive it as: get all the permutations of m items, then, because we only care about the first n items picked, we don't care about the order of the m-n other items so we divide by (m-n)!. Likewise, if you also don't care about the order of the first n items, you divide by n!

That's brilliant, thanks. One thing that I always loved about maths and the harder sciences is the way that you can think a problem through in different ways and they all give the same answer.
xtifr wrote:... and orthogon merely sounds undecided.


Return to “Individual XKCD Comic Threads”

Who is online

Users browsing this forum: Reka and 102 guests