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  #21  
Old 08-28-2015, 11:59 AM
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Originally Posted by Daekyras View Post
I was working on that little bit assuming that 8th could then be added on to. I.e. It would flow from there. Damn, I hate being bad at things!
This really is the tedious part. It's easy to make a minor error here. More often than not they use computers to convert flowcharts. The cool part will come when we convert to Subset-Sum (maybe we'll convert to 3-coloring graphs as well, those are pretty cool).


The even cooler part is the one where we see all of these problems are NP Complete. IOW, if you can find a way to solve any one 'fast', you can solve them all 'fast'. Which would lead to cures for cancer, mathematically perfect spaceships, and the ability for a computer to prove any mathematical statement that can be expressed formally, assuming the proof exists.
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Old 08-28-2015, 12:03 PM
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This really is the tedious part. It's easy to make a minor error here. More often than not they use computers to convert flowcharts. The cool part will come when we convert to Subset-Sum (maybe we'll convert to 3-coloring graphs as well, those are pretty cool).


The even cooler part is the one where we see all of these problems are NP Complete. IOW, if you can find a way to solve any one 'fast', you can solve them all 'fast'. Which would lead to cures for cancer, mathematically perfect spaceships, and the ability for a computer to prove any mathematical statement that can be expressed formally, assuming the proof exists.
You're right. I haven't done anything like this in so long I thought it would fit like an old glove but instead it fits like a new glove.

Yup, I never really got that metaphor.

Also, despite my warnings in a previous thread I appear to be the one who is seduced by the maths. Irony thy name is boolean!
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  #23  
Old 08-28-2015, 12:38 PM
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You're right. I haven't done anything like this in so long I thought it would fit like an old glove but instead it fits like a new glove.

Yup, I never really got that metaphor.

Also, despite my warnings in a previous thread I appear to be the one who is seduced by the maths. Irony thy name is boolean!
Lol. I didn't think your warning was serious.

In any case, this tattoo one can be written in disjunctive normal form fairly easily, since there are only a handful of paths through. We can still get the conjunctive though, just give me a second. Normally finding the disjunctive normal form is the hard part (to put it in context, if it were easy to find DNF for an arbitrary Boolean sentence, secure internet traffic would be impossible). But since we are looking for different ways to express the problem, and not the solutions, it's a bit trickier.

Do you do anything with eigenanalysis or cosine integrals in your work?
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  #24  
Old 08-28-2015, 04:01 PM
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Okay...I think I've got it (though a second pair of eyes to double check it is welcome):

NOT (A OR B) AND D AND NOT (E AND F) AND G AND NOT H AND NOT (K AND (L OR M)) AND N AND (NOT O OR (P AND (NOT Q OR R)))

Here's the chart again:

I'll add the legend in a second.

ETA:
A= Are you drunk?
B= Are your friends egging you on?
C= Are your friends laughing?
D= Does it have a special meaning?
E= Is it a name?
F= Is it the name of a significant other?
G= Is it unique?
H= Is it 'Steve-O' unique?
I= Are you trying to fit in?
J= Are you sure you are not trying to fit in?
K= Will it be visible when you are dressed?
L= Are you a white collar worker?
M= Will it be on your face?
N= Is it appropriate for children to see?
O= Is it going on the small of your back?
P= Do you want men to think you are easy?
Q= Are you a man?
R= Do you prefer to 'catch'?
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  #25  
Old 08-28-2015, 04:11 PM
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Obviously some of the variables are superfluous.
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  #26  
Old 08-28-2015, 04:20 PM
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NOT (A OR B OR H) AND NOT (E AND F) AND NOT (K AND (L OR M)) AND (NOT O OR (P AND (NOT Q OR R))) AND NOT (NOT D OR NOT G OR NOT N)

Here it is compressed a bit...

Now to CNF SAT
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  #27  
Old 08-28-2015, 04:55 PM
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Okay, I cheated a bit and just used Wolfram Alpha to convert to CNF SAT.



I think it's right? Again, another set of eyes is welcome. And if anyone wants to try converting to 3-SAT, this is the easy step (especially since no clause has more than three literals, so just invoke some X and Y that are always false to round out the terms).


I think from here on out, we'll change the terminology a bit, so 'A' will be A, but 'a' will be NOT A, and so on. X and Y are both always FALSE. 'v' is OR, '^' is AND. Just to make everything nice and neat.

And, since 3-SAT is typically the glue that holds NPC problems together, we find ourselves at a crossroads. We can convert to a graph coloring problem, which is very cool visually but far removed from the numerical tools I wanted to end on. Or we can stick with the original plan, reduce to subset-sum, and then end with f(z)=alpha-beta*z^2, where pairs of {z,f(z)} that are both natural numbers correspond to an acceptable assignment of the original variables.
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  #28  
Old 08-28-2015, 05:04 PM
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The basic tools for the 3-coloring construction, if anyone wants to take a crack at it:




The basic rule is that (using three colors), each node must be colored a color that is different than the colors of the adjacent nodes (iow, nodes that share an edge).

Since X and Y are fixed, you will need to add two new edges to that effect (x to TRUE, y to TRUE).
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  #29  
Old 08-28-2015, 05:12 PM
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Whoops, didn't save the image from Wolfram Alpha the first time.

Here it is:

Again, a second set of eyes is welcome.

And, if people feel like running it through Wolfram Alpha themselves, here is the text of the input:
BooleanConvert[! (A || B || H) && ! (E && F) && ! (K && (L || M)) && (! O || (P && (! Q || R))) && ! (! D || ! G || ! N),"CNF"]
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  #30  
Old 08-28-2015, 05:24 PM
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And now the 3-SAT...

(PvovX)^(evfvX)^(kv(lowercase L (yeah,didn't think that through))vX)^(kvmvX)^(Rvovq)^(DvXvY)^(GvXvY)^(NvXv Y)^(avXvY)^(bvXvY)^(hvXvY)

ETA: actually, since 'I' is superfluous, maybe I can take out the commentary on 'l'.

ETA2: why is there a space between '(NvXv' and 'Y)'?

ETA3:
3-SAT in a Wolfram friendly form:
(P || o || X) && (e || f || X) && (k || l || X) && (k || m || X) && (R || o || q) && (D || X || Y) && (G || X || Y) && (N || X || Y) && (a || X || Y) && (b || X || Y) && (h || X || Y)

ETA4:
Actually Wolfram didn't read it right this time around...idk why.


Anyway: Subset-Sum (with this as the endgame) or Graph Coloring (see below)?
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  #31  
Old 08-29-2015, 12:20 AM
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Originally Posted by The Unreasoner View Post
NOT (A OR B OR H) AND NOT (E AND F) AND NOT (K AND (L OR M)) AND (NOT O OR (P AND (NOT Q OR R))) AND NOT (NOT D OR NOT G OR NOT N)

Here it is compressed a bit...

Now to CNF SAT
That is Wat I was trying to write earlier. That is good TU. It's funny, it speaks to that part of my brain that hides St the back and says "everything should be in the right place. That's when stuff works". Unfortunately the other part of my brain that says "but what if I replace k with dark matter. Maybe shit will explode!!" Tends to take over.

As for eigenanalysis- yes. It occurs in a lot of the 3d "space" work in theoretical physics.
I've moved aside from that in recent years but we still work with matrices from time to time in particle. And the more I see you post the more impressed I am with your maths.
You might finally crack that FBI code!
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  #32  
Old 09-16-2015, 02:03 AM
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Originally Posted by Daekyras View Post
That is Wat I was trying to write earlier. That is good TU. It's funny, it speaks to that part of my brain that hides St the back and says "everything should be in the right place. That's when stuff works". Unfortunately the other part of my brain that says "but what if I replace k with dark matter. Maybe shit will explode!!" Tends to take over.
It really is incredibly satisfying to take some tangled knot of information and untie it, putting everything in its proper place. Or even better: finishing some elaborate domino construction, and having it just work, from start to end (on that note, this is always worth a watch). This isn't quite like dominos, but it's certainly close. Actually you can build AND and OR gates with dominos (and XOR, which makes me think NOT gates can be done as well), so if you really wanted, you could convert that Boolean sentence into a massive domino setup (though you'd need to push all the TRUE input dominos at the same time (or at a fixed interval) to make it work), where the last domino only falls when the sentence is TRUE.

I also have that anxious naysayer part of my brain, though its fears are rarely expressed as artfully as yours. It's more of a general anxiety/unease that I attribute to my sporadic OCD.
Quote:
As for eigenanalysis- yes. It occurs in a lot of the 3d "space" work in theoretical physics.
I've moved aside from that in recent years but we still work with matrices from time to time in particle.
Eigenanalysis just has so many applications. For a little while after college I helped one of my professors develop some heuristic methods to try and get some speed-up (because the current algorithms are so slow) in specific sub-fields. We actually did get a decent speedup in most of them, but they were all only probabilistic in terms of success. And the speedup was not big enough for it to really make sense to run the heuristic first, except in a few cases. Couldn't get a buyer for any of them.

Quote:
And the more I see you post the more impressed I am with your maths.
You might finally crack that FBI code!
Lol. Well, you were born polite and charming. As it happens, I am quite good at math, and in a few fields I may even be great. But I don't think I've posted anything here (at least not yet) that shows my ability matches my enthusiasm. I think the thing I take the most pride in (in all academic disciplines) is my ability to ask good questions.

I may very well be the one to crack the Kryptos. But I've stopped trying recently, and smarter people have tried and failed. But undoubtedly my interest will swell again, and I'll have new ideas to test. And new ideas about why my previous efforts (or methods) failed. I know if I read in tomorrow's paper that Kryptos was cracked and it was encrypted in a manner I considered, I'll reproach myself for the rest of my life for lacking perseverance. And I still think there's a chance Sanborn reads Theoryland. What are the odds that he releases a new clue the day after I start the thread?

As for my possible mathematical greatness: for the last six years I have worked (sporadically) on the Goldbach conjecture. I have brought new info to bear on the problem, though I guard it jealously (paltry though it is). Essentially, I have found some evidence that a certain primality test can be expressed in a more general way with an infinite series, which would let me bring in some of the powerful numerical tools available in complex analysis to attack the problem. Unfortunately, most of my new info is only held up by statistics (lacking the rigor and elegance one would hope for in an argument's foundation). And naturally pseudoprimes throw a big wrench (or small pinch of dark matter) into the mix. So my possible greatness will depend in a large part on my ability to 'intuit' the true definition of a curve that is now, at best, loosely bounded in one dimension and in one direction.


In any case, I still mean to finish out this thread (or at least my part in it). After I close out this specific problem, I'll make a few posts on nondeterministic polynomial time, P vs NP, PSPACE, and of course the money shot: applications.

I originally intended to turn the thread over to Sodas as a sort of peace gesture, hoping he could walk us through some aspects of solar power. But he seems to have vanished again. So, Daekyras (or anyone else reading this thread), would you be interested in walking a small but engaged audience through some topic you are interested in?
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  #33  
Old 10-18-2015, 04:21 PM
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So I finally got around to converting to subset-sum, and something occured to me:

Generally, you work in base 10 with numbers of the form 1000101001 or something like that, summing them to a number of the form 1111333333. Now, there are no cases when the numbers carry from column to column while having a TRUE corresponding answer. Does this mean I can treat the numbers as base 4 instead, and convert to base 10? So something like 11133 would be 351 instead. It would make the last conversion more approachable. I've proved that you don't lose any solutions doing this, but I think it might introduce some false positives.
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Old 10-18-2015, 07:35 PM
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For context, I'm trying to reduce the problem size (to make finding quadratic residues in the last step a little easier). This subset sum has a multiset, with numbers ranging from 1 to something on the order of 10 to the number of variables in 3 SAT. But it turns out the important (and largest) members are taken in pairs, where you have to choose one. So what if I replace each of those pairs with one number, with the value of the larger minus the smaller. You'd also subtract the summation of the minimums from the target. You'd cut down the numbers by a substantial amount, and seriously reduce the size of the set as well.
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Old 10-19-2015, 09:30 AM
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Wouldn't using hexadecimal numbers make more sense in this case?
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Old 10-19-2015, 06:19 PM
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Originally Posted by GonzoTheGreat View Post
Wouldn't using hexadecimal numbers make more sense in this case?
I don't think so. How do you mean?

Anyway:
3-SAT to Subset-Sum:
Choose a subset of the following numbers that sums up to 33333:
z01=1
z02=1
z03=1
z04=1
z05=10
z06=10
z07=10
z08=100
z09=100
z10=100
z11=110
z12=1000
z13=1000
z14=1000
z15=1000
z16=10000
z17=10000
z18=10000
z19=10001

Any subset with such a sum corresponds to a satisfactory assignment of the variables, decoded as following:
A is always FALSE
B is always FALSE
C is redundant (can be either TRUE or FALSE without affecting the solution in any way)
D is always TRUE
E is TRUE iff z12 is not a member of the subset
F is TRUE iff z13 is not a member of the subset
G is always TRUE
H is always FALSE
I is redundant
J is redundant
K is TRUE iff z11 is not a member of the subset
L is TRUE iff z08 is not a member of the subset
M is TRUE iff z05 is not a member of the subset
N is always TRUE
O is TRUE iff z19 is not a member of the subset
P is TRUE iff z16 is a member of the subset
Q is TRUE iff z01 is not a member of the subset
R is TRUE iff z02 is a member of the subset


As you may note, the target is a series of threes (though I got rid of the leading ones). This indicates that either a variable or its negation appears in the Boolean statement, not both. You may also note that many of the numbers in the multiset are repeated. What is cool is that this does not matter. Play around with this if you want, and you will see (you could just look at the flowchart and take a known successful path and then find the subset aided by that info).

And the legend again:
A= Are you drunk?
B= Are your friends egging you on?
C= Are your friends laughing?
D= Does it have a special meaning?
E= Is it a name?
F= Is it the name of a significant other?
G= Is it unique?
H= Is it 'Steve-O' unique?
I= Are you trying to fit in?
J= Are you sure you are not trying to fit in?
K= Will it be visible when you are dressed?
L= Are you a white collar worker?
M= Will it be on your face?
N= Is it appropriate for children to see?
O= Is it going on the small of your back?
P= Do you want men to think you are easy?
Q= Are you a man?
R= Do you prefer to 'catch'?
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Old 10-19-2015, 08:16 PM
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So I'm trying to close this out, but I haven't done this in a while, and have run into a problem.
Here's the link to convert to a Quadratic Diophantine problem:this.


Now, I've got most of the variables, but can't see how to get s (because of the ambiguity in sigma). Does anyone know what it should be? Or at least what I should do?

Here's what I've got so far:
t=33333

H=943974885486627996376585908199285766702474153268 63566166970396747975999240862245882753680067208887 50835306795438968702807914763892215557094897586510 35382954068249265988256844456413991099326536651938 27015782801311615153724985195711581486850455416474 16996313276667119578616496492220667240804492176514 18966373051530933289919606631185892738899545880172 30004063961078326601299852365476748417726567298301 95267918669177995343639425150991046689224644923123 15265445845852858969145592524293453987307554974454 1

K=292149281968973323871782335698164924792839334640 12830777385768029820977803396466280266248955183183 56952928322449090020404791651692374307748151155709 32615436861699033757797247274214733059193449575011 61593482950448709121252538490017034317633015060883 38951873648448857389898615651855524379857440299341 20389499400320532054741479455771482954957665182878 80728464527454529219087824671722119369172808698628 69230992174795499320738109255915928774796713151352 08289273376165943547922092327752561531383323669433 59375

m=19 (yes, probably too big, but I wanted a margin for safety. I thought I'd test it at smaller numbers after I got it to work on 19)

n=19

q=[3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]

x (the list, not the parameter)=[1, 1, 1, 1, 10, 10, 10, 100, 100, 100, 110, 1000, 1000, 1000, 1000, 10000, 10000, 10000, 10001]

theta=[94397032522381825655184531838587189453496419295890 17754961180960916258118764004711994351438718434206 58167320229032178137964425579813135030182010814470 24633893742703625600741041005255203717914573906662 31196823024727078992372339467300850195199759624491 60611793569968153353496679687717360362290138157780 85322168127744467647975407154987854714585096404551 25445793605408547425809794177058809795787329058649 53600868465233744524811204186573801311381213993144 0759191318758105737855497093282256259918212890625, 44877384580642632714783821154854025987387029798891 65390035684517508414589693922197087300239427696566 74982805736972031139984129932315196615363556598756 39359882452900197536636851386934697138894296046713 36100433573690624146554881148238369769807980888443 73922655900286701622471111389819745365881747304076 71454461748792622694376965798094066665676510032907 07365892927731802256463233321724151843489694671815 60490044840127153298765843472479929881166603204504 72404166368485598877814007324068021838807041, 72515660551491889364007644314641795597721117629174 81192460114090077619712377592719049219393832198065 24138507500623641880465290719896257659841986358025 25129283757315365381153085219856740880452040070957 21548564778055578751364475738661333494029537113220 95458503055888741471190453290555508807851899335096 28837819575184588313604764928721230755730588137162 99542476537199702155871537033425621994892148907062 97162988325284756459853565670904294615762628212572 099357802756696397612262256259918212890625, 78247588023389668646285724460300983130275459124864 46080479390101247117033321020279004773511954517162 93317879017034591011388404600566474830270318173401 22482242964238302467954700367557829000709558242603 61532603834978276861404839102023856554793730709931 50608156227533527227772370572992085708617231093451 67647514765469886117025318209859380642354881907079 88326771717847620184681308419667686083976547256460 75537720757349150487484794930910441977671303558490 41387820469765516292256259918212890625, 86538056553541570631197290094756829851853968889050 07223383962610415316759390746342327395144589949784 03165267277990260734718682444462897285008915449259 98609184264372294788804222502575509109888692052464 26229929314160295081356761106012460904852324477825 60636898154079382179551157284632133480161768305639 15344062303948165769583698649379284314897596275396 69476581828418915531667738881016753107340880545095 77441160846514076548013211424843242649945827544315 8010806356180362342562599182128906250, 49572121262700015154654210920804211603363127079033 53763787258247317574240791743412780724288735008070 70604737478428072192594465656261870535087706496039 08458464306623170087556152420833581732574416454239 92684329413849211554251486321912893600032016677267 88743460170538184773068258285380790309996259697525 46663957749727052883253951387963205787027613703052 26147721966934678157441260697997745768101628623351 83102876424963803948868685240958027121469947294895 1051646566676382562599182128906250, 47280046240261540397891335035056325450998443292555 60667658677235233142931412509028548416111617806278 38867912134608346951441143002676599976022375762278 37181546355497419901245742330984365961003475548779 06684225384304431034985599125802765628985287194239 31867208944556521661586999675426372926673639479811 97633507495050894963637301901537964316704827739695 44193934370839553462959498076255340097627835484307 87256873301271437853882524258051957377041764061178 7691605469371932562599182128906250, 16032616010641861938009693712728546628767511667643 97435193023809577914019987558697300539509953451997 40153057045739723002780992940667878333594223195962 84434971438168787066267538128701198393274109232217 83088306598450871189107613378722006420295550089783 25442279242983393880370409026883835429616280787107 93950879291897201878356999476472462075097698518449 91617684845246532623799979513588419726948400450835 28048446293930946080845979673212185481099106048097 398738931375365625991821289062500, 92984029403533462161187055124147279381581035405969 35469707169323837286453304388891041751987787715005 04955514961586211443625465915168001295192018577769 10147578479558786989190395499051338934728782850698 06758905916742077323223796464422107700694446174457 04174673768399912510588341393076294761600721495419 74043342386125890826944105191416253792325496315556 57482933049331756711816421326347752188086104440274 27753947061463551538784915850584304219851710145105 132045862165625991821289062500, 52290831605769128051039325701066216341575515886896 19782904790148923009587948655816050315747109491533 64754518827760240465938194584967615479142483411085 00202735080376292173999760626288892805806002151782 98752846808873998537979452323212932122728203450162 89658493310063595458622158998497399459017828108797 43725686431914167463442405207131220847512272334980 28897297931656198484755835401608276730647836254364 44865573830096962145108997591799278358105939143129 836891740055625991821289062500, 18743439366635453098332467226732535749652194094466 87576712828313688265737759489487895235296713818449 50261018540542774382021804166049564509940243960082 33894792728212661966474205952807046613873610289506 87272041805124082132576800527720112773131700204525 49229599155092603378636247746340426315340590802771 77382996741593841148163501996567954081513968171637 47550749671225824527927463477894462137882261099244 84726987184756286086725418312828172914152472455605 68398053228188591003417968750, 24897139427146452486360712577443338579199734734755 24370981315120737708655284439391024599251493310121 29327299318423159379219903884338875544984485230628 97796623970597387093197844237948614777597731690442 89879020619480155706889534988587174562618009705958 40097586420725711122185926219731842705604654821821 14369092472623507613280610959409973636631178593763 57121280533228997072121117445357900026041502912335 20292515709970098333813062835357886163831192828302 6473123946259918212890625000, 10485534309213614561005768939573398241978086111113 78861514009781110344532177264850913306966261803736 07017937555934010381250973873410010494602446736581 70988510271585258820254620720075488762298594643968 43978632485437284351425509034483215846385148650196 20056307846951695272319674377861865792790300396792 41400873543076919532621215687948981020109285861601 04279473196853347391564969755353890535469492286579 14350905589530748622299959971825133929484511470694 263581166259918212890625000, 46235440786818833355076103193304099687817642206722 75401895778555099711941078463876974921350762392247 13928338592686955747494583870087044112706599039355 44693195379338522907018587136495364484872206890691 63890609371540526506386534116749159346759117940976 68502398740332624609343290016696419335130510589268 35355072216775193975024511749554037546748762144252 51489746925305718596231666152396157333677896207392 02214054083777346319097959096900553602998664037600 37082106259918212890625000, 84332813017385050960522142355796265250603236300749 99957873546893136647158026760752382233733480276560 02078988238560089595030797001362028490343266322048 23715545283434315071557153306440399704270053834369 90867632097271858265601002884213714401429817788082 05024536478162550082512413521172834086536848319752 76236290589155063445947938825646410269794718323149 13275424183584944834877868654795698413204649118555 86803652975217930278084113162494949098089432822439 5816116259918212890625000, 16887879812171436893272869423305692769465562794154 26904074993359587332411233943370540232677915430966 41157255236813975153735537797177027451904917436311 70138243894242033560398875788933204418622788636912 57081263144191690756941870152920532593635786342117 79217080713412754033619423409169796903231885700603 54150178021821784727236062569829483315327902497889 27842090011405922125299344903337866636884551252323 19512491833485765514504430668414584472048554144923 4596802599182128906250000, 73237502913176108634548716278892701327626975092647 30815661220588910895175841655504548237898674127883 31491372817484758091140946871902395312848770211495 50502087865120314213804594322562569637189363252969 62524650022323223592198888304670755662348012774297 64977391235805713609817476138847187451907690284991 75596319523639797925935606684511119485840922988779 41228840835947426898031922116019090568280848435947 14372594163096571310243516525879835882017039661267 67072599182128906250000, 16744368241542054611659215781031162653439660929862 26134470455265318590818152894663971583984486546788 21862302317368760533898850653737406360018647933306 73920730729593497615509881648163392932331077776708 68952185540314544016783567971978452090931367163765 09305973213107955632173778877964641376849810327749 13051662337864428337685118300161581476290173822362 62797256365995997550619377286438427784440489248256 11664561765001258882424202563994871153428416579559 526962599182128906250000, 29016237393416209248230478234166540659738995216817 34224720330149125901954409648393043097866426188618 46215252684501796045954068598059289873971077192060 45427415510617730900250909423239804235166943039322 40623824552495284894735750828080315532976575849809 89410851262808138411429398695756805969652118331950 81149199056316298378602942940735544860005977701103 20520428668507962270138170556872062598652789288929 72484000171411031758405721577766330022279992508132 71444855442047119140625]

Any thoughts?
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  #38  
Old 10-19-2015, 08:24 PM
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Here's f(z) in its current form:
f(z)=(1/1048576)*lambda[2]*s^2-(1/29214928196897332387178233569816492479283933464012 83077738576802982097780339646628026624895518318356 95292832244909002040479165169237430774815115570932 61543686169903375779724727421473305919344957501161 59348295044870912125253849001703431763301506088338 95187364844885738989861565185552437985744029934120 38949940032053205474147945577148295495766518287880 72846452745452921908782467172211936917280869862869 23099217479549932073810925591592877479671315135208 28927337616594354792209232775256153138332366943359 375)*z^2*lambda[1]-(1/1048576)*z^2+(891088584429492439071543005627573185 20974348491224338340691107127701808163319545709499 88849127188728811522964840210472681071618719391370 10930285961843535641183905970164159849691696719092 83098262924929995106060899747325130125101538649963 68394220928473716636070069083991321888596875152990 79567540689832103800164436206829271435859864478842 17176857278273142958788212456401768353762606905526 40124704149111513121122074202517751589402672303185 97913232677880553808992665590338196791419393892718 12340702276034800235334715306370765600215885887501 39096010512407005704911880208240035974301433280035 62565232276770110865115702202504667939624913442167 14577839463597999800353737990556304381365157657085 04355108191005469381741938368605120356460400420223 92472403360179264737623903019276083462754041295899 58053545873850278249948881864484796155053572766425 20084091551935419963073879624152997978120781497062 67008543649422167687292166916648741226433107713851 33751649989710480874254715631155851834186764930486 210359300681/29214928196897332387178233569816492479283933464012 83077738576802982097780339646628026624895518318356 95292832244909002040479165169237430774815115570932 61543686169903375779724727421473305919344957501161 59348295044870912125253849001703431763301506088338 95187364844885738989861565185552437985744029934120 38949940032053205474147945577148295495766518287880 72846452745452921908782467172211936917280869862869 23099217479549932073810925591592877479671315135208 28927337616594354792209232775256153138332366943359 375)*lambda[1]
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  #39  
Old 10-19-2015, 09:58 PM
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So it turns out there are 1,320 different solutions to the original problem (out of 262,144 possibilities). Which means (if assignments are chosen randomly) you'd expect to be able to get a tattoo 0.503540039% of the time. Not bad (it at least makes search efficient).

Of course, several variables are fixed, and three are irrelevant. So the number of variables you actually have to solve for is 9. Which can take 512 possible forms, and leads to a satisfactory solution 165 times. Which means a 32.2265625% chance of success when randomly choosing only these nine variables [E,F,K,L,M,O,P,Q,R]. Which just shows the importance of reducing the problem when possible.

If you want, I've constructed a truth table you can look at. Simply create a nine-digit binary number with the digits corresponding to the true/false values of [E,F,K,L,M,O,P,Q,R] (true=1,false=0), convert to decimal, then look up the position+1.

Here:
[true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, true, true, true, true, true, true, true, true, false, false, false, false, true, true, false, true, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false]
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Last edited by The Unreasoner; 10-19-2015 at 10:01 PM. Reason: added color
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