Hardest Math Problem Ever

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MigElite

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#1 MigElite
Member since 2004 • 1304 Posts
If in a computer there's 15 different programs and you can only use 5 each day, how many different combinations are there?
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johndoh4

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#2 johndoh4
Member since 2003 • 1743 Posts
a lot
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PowerSerj

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#3 PowerSerj
Member since 2008 • 745 Posts

If in a computer there's 15 different programs and you can only use 5 each day, how many different combinations are there?MigElite

How come only 5 programs a day can be used? That seems pretty counterproductive.

Anyways my answer is 3.

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deactivated-59d151f079814

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#4 deactivated-59d151f079814
Member since 2003 • 47239 Posts
15 X 14 X 13 X 12 X 11
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cricket_foreva

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#5 cricket_foreva
Member since 2006 • 306 Posts

If theres actually an answer, im going to go with 3003??.

From what i can see, its a statistical question.

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entropyecho

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#6 entropyecho
Member since 2005 • 22053 Posts
15C5 = 360,360?
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entropyecho

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#7 entropyecho
Member since 2005 • 22053 Posts

15 X 14 X 13 X 12 X 11sSubZerOo

Good for you! A Combinatorics expert!

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Shadowhawk000

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#8 Shadowhawk000
Member since 2007 • 3453 Posts

[QUOTE="sSubZerOo"]15 X 14 X 13 X 12 X 11entropyecho

Good for you! A Combinatorics expert!

Wha...Huh *brain explodes*

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UnrighteousFury

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#9 UnrighteousFury
Member since 2008 • 2764 Posts

[QUOTE="sSubZerOo"]15 X 14 X 13 X 12 X 11entropyecho

Good for you! A Combinatorics expert!

Witchcraft!

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deactivated-59d151f079814

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#10 deactivated-59d151f079814
Member since 2003 • 47239 Posts

[QUOTE="sSubZerOo"]15 X 14 X 13 X 12 X 11entropyecho

Good for you! A Combinatorics expert!

Yeah isn't that like basic pre calc? Or maybe even Algebra? I can't remember havn't taken a math course in over a year or two.

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MigElite

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#11 MigElite
Member since 2004 • 1304 Posts
urgh...lol this is hard that's a problem someone invented that i need to solve, i mean i dont really now of its possible or not so yeah...
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edgewalker16

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#12 edgewalker16
Member since 2005 • 2286 Posts

Hardest math problem ever?

Recite pi, in it's entirety, from memory...backwards!

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loco145

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#13 loco145
Member since 2006 • 12226 Posts

Hardest math problem ever?

Recite pi, in it's entirety, from memory...backwards!

edgewalker16
Um, we should stick to problems with a solution. ;)
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spyrofan_sp

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#14 spyrofan_sp
Member since 2008 • 323 Posts
[QUOTE="entropyecho"]

[QUOTE="sSubZerOo"]15 X 14 X 13 X 12 X 11Shadowhawk000

Good for you! A Combinatorics expert!

Wha...Huh *brain explodes*

he used 8th grade math. its simple. once you learn the conditons and stuff you have to use it under anyway

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HardQuor

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#15 HardQuor
Member since 2007 • 1282 Posts
If i'm not mistaken, 15*14*13*12, etc.. will only give you the number of possible arrangements of 15 programs. ---edit--- OIC what you did thar.
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black_cat19

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#16 black_cat19
Member since 2006 • 8212 Posts

15C5 = 360,360?entropyecho

This. ^^

It only takes a second with a calculator.

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RyuHayabusaX

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#17 RyuHayabusaX
Member since 2005 • 7838 Posts
Simple SAT Math question, for Math II that is, maybe not for Reasoning.
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chad_daddy

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#18 chad_daddy
Member since 2008 • 500 Posts
ok that's easy just takes a minute or two
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kayn83

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#19 kayn83
Member since 2004 • 2214 Posts

Hey math people...

How does realism differ from constructivism and liberalism?

What are some supporting evidence for the ontological argument of God?

Why can some of Boaz' theories be deemed racist?

Yeah exactly, you don't know that.

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GamerBoy53

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#21 GamerBoy53
Member since 2008 • 2666 Posts
Is it 75???
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VacantPsalm

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#22 VacantPsalm
Member since 2008 • 3600 Posts

[QUOTE="entropyecho"]15C5 = 360,360?black_cat19

This. ^^

It only takes a second with a calculator.

Oh my crap I just typed 15 into my calculator and erased it with C. Damn that fail was hard.:cry: And btw, I think you guys just helped this kid with his homework. Calling something "the ______est ever" online = someone WILL prove you wrong.
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boshlonavish

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#23 boshlonavish
Member since 2005 • 1229 Posts
IT'S A TRAP.
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Tuky06

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#24 Tuky06
Member since 2007 • 5026 Posts
Hardest? If I weren't this lazy right now I would answer with only using 5th grade mathematics.
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#25 fighter91
Member since 2005 • 1293 Posts
[QUOTE="entropyecho"]

[QUOTE="sSubZerOo"]15 X 14 X 13 X 12 X 11sSubZerOo

Good for you! A Combinatorics expert!

Yeah isn't that like basic pre calc? Or maybe even Algebra? I can't remember havn't taken a math course in over a year or two.

i actually learned combinations in algebra 2 lol. our teacher took like 20 minutes to explain it since it was so easy.

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Shad0ki11

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#26 Shad0ki11
Member since 2006 • 12576 Posts
[QUOTE="edgewalker16"]

Hardest math problem ever?

Recite pi, in it's entirety, from memory...backwards!

MoonMarvel

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812314593571984922528471605049221242470141214780573455105008019 086996033027634787081081754501193071412233908663938339529425786 905076431006383519834389341596131854347546495569781038293097164 651438407007073604112373599843452251610507027056235266012764848 308407611830130527932054274628654036036745328651057065874882256 981579367897669742205750596834408697350201410206723585020072452 256326513410559240190274216248439140359989535394590944070469120 914093870012645600162374288021092764579310657922955249887275846 101264836999892256959688159205600101655256375678566722796619885 782794848855834397518744545512965634434803966420557982936804352 202770984294232533022576341807039476994159791594530069752148293 366555661567873640053666564165473217043903521329543529169

Now just reverse it. ;)

^^How's that?^^

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Acemaster27

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#27 Acemaster27
Member since 2004 • 4482 Posts

If the order of the programs doesn't matter than there are 3003.

If the order of the programs does matter each day there are 360,360

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momo372

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#28 momo372
Member since 2005 • 2641 Posts
a lotjohndoh4
i had a similar maths problem and I wrote "alot" as my answer. Ended up passing
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Stesilaus

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#29 Stesilaus
Member since 2007 • 4999 Posts

If in a computer there's 15 different programs and you can only use 5 each day, how many different combinations are there?MigElite

I've seen several posters proposing an answer of 15 x 14 x 13 x 12 x 11. That's wrong, because it gives the number of permutations, not the number of combinations! I'm pretty sure you have to take that number and divide it by the number of different permutations of the chosen programs, i.e. 5 x 4 x 3 x 2 x 1.

So my answer would be (15 x 14 x 13 x 12 x 11) / (5 x 4 x 3 x 2 x 1), which you can write more succinctly as 15! / (10! x 5!).

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ChrisSpartan117

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#30 ChrisSpartan117
Member since 2008 • 4519 Posts
Tell me what pie is when multiplied by itself.
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Tuky06

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#31 Tuky06
Member since 2007 • 5026 Posts
Tell me what pie is when multiplied by itself.ChrisSpartan117
A squared pie?
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Acemaster27

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#32 Acemaster27
Member since 2004 • 4482 Posts

Tell me what pie is when multiplied by itself.ChrisSpartan117

A square pi.

6.blahblahblahblahblah

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felixworks

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#33 felixworks
Member since 2005 • 337 Posts

0/0

Oh god what have I DONE?!?!?!?!

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#34 VacantPsalm
Member since 2008 • 3600 Posts

[QUOTE="ChrisSpartan117"]Tell me what pie is when multiplied by itself.Acemaster27

A square pi.

6.blahblahblahblahblah

Uhh, you mean 9.blablablablablabla.
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#35 eckboxes02
Member since 2007 • 226 Posts

If you can only use one combination a day, then i guess there's only one combination of five numbers.

per day, but how many day's do i got?

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#36 69ANT69
Member since 2007 • 8472 Posts
My mind just melted.
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#37 pikma
Member since 2004 • 483 Posts

[QUOTE="MigElite"]If in a computer there's 15 different programs and you can only use 5 each day, how many different combinations are there?Stesilaus

I've seen several posters proposing an answer of 15 x 14 x 13 x 12 x 11. That's wrong, because it gives the number of permutations, not the number of combinations! I'm pretty sure you have to take that number and divide it by the number of different permutations of the chosen programs, i.e. 5 x 4 x 3 x 2 x 1.

So my answer would be (15 x 14 x 13 x 12 x 11) / (5 x 4 x 3 x 2 x 1), which you can write more succinctly as 15! / (10! x 5!).



But the results can't be combinations in this case, since you'd be working with 5 different programs each day, this means that after you run a program, you can't run it again the same day, that would make a permutation. Combinations are used when the events aren't mutually exclusive.

15P5 = 360,360
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#38 Funky_Llama
Member since 2006 • 18428 Posts
[QUOTE="MoonMarvel"][QUOTE="edgewalker16"]

Hardest math problem ever?

Recite pi, in it's entirety, from memory...backwards!

Shad0ki11

-3.1415926535897932384626433832795028841971693993751058209749445 923078164062862089986280348253421170679821480865132823066470938 446095505822317253594081284811174502841027019385211055596446229 489549303819644288109756659334461284756482337867831652712019091 456485669234603486104543266482133936072602491412737245870066063 155881748815209209628292540917153643678925903600113305305488204 665213841469519415116094330572703657595919530921861173819326117 931051185480744623799627495673518857527248912279381830119491298 336733624406566430860213949463952247371907021798609437027705392 171762931767523846748184676694051320005681271452635608277857713 427577896091736371787214684409012249534301465495853710507922796 892589235420199561121290219608640344181598136297747713099605187 072113499999983729780499510597317328160963185950244594553469083 026425223082533446850352619311881710100031378387528865875332083 814206171776691473035982534904287554687311595628638823537875937 519577818577805321712268066130019278766111959092164201989380952 572010654858632788659361533818279682303019520353018529689957736 225994138912497217752834791315155748572424541506959508295331168 617278558890750983817546374649393192550604009277016711390098488 240128583616035637076601047101819429555961989467678374494482553 797747268471040475346462080466842590694912933136770289891521047 521620569660240580381501935112533824300355876402474964732639141 992726042699227967823547816360093417216412199245863150302861829 745557067498385054945885869269956909272107975093029553211653449 872027559602364806654991198818347977535663698074265425278625518 184175746728909777727938000816470600161452491921732172147723501 414419735685481613611573525521334757418494684385233239073941433 345477624168625189835694855620992192221842725502542568876717904 946016534668049886272327917860857843838279679766814541009538837 863609506800642251252051173929848960841284886269456042419652850 222106611863067442786220391949450471237137869609563643719172874 677646575739624138908658326459958133904780275900994657640789512 694683983525957098258226205224894077267194782684826014769909026 401363944374553050682034962524517493996514314298091906592509372 216964615157098583874105978859597729754989301617539284681382686 838689427741559918559252459539594310499725246808459872736446958 486538367362226260991246080512438843904512441365497627807977156 914359977001296160894416948685558484063534220722258284886481584 560285060168427394522674676788952521385225499546667278239864565 961163548862305774564980355936345681743241125150760694794510965 960940252288797108931456691368672287489405601015033086179286809 208747609178249385890097149096759852613655497818931297848216829 989487226588048575640142704775551323796414515237462343645428584 447952658678210511413547357395231134271661021359695362314429524 849371871101457654035902799344037420073105785390621983874478084 784896833214457138687519435064302184531910484810053706146806749 192781911979399520614196634287544406437451237181921799983910159 195618146751426912397489409071864942319615679452080951465502252 316038819301420937621378559566389377870830390697920773467221825 625996615014215030680384477345492026054146659252014974428507325 186660021324340881907104863317346496514539057962685610055081066 587969981635747363840525714591028970641401109712062804390397595 156771577004203378699360072305587631763594218731251471205329281 918261861258673215791984148488291644706095752706957220917567116 722910981690915280173506712748583222871835209353965725121083579 151369882091444210067510334671103141267111369908658516398315019 701651511685171437657618351556508849099898599823873455283316355 076479185358932261854896321329330898570642046752590709154814165 498594616371802709819943099244889575712828905923233260972997120 844335732654893823911932597463667305836041428138830320382490375 898524374417029132765618093773444030707469211201913020330380197 621101100449293215160842444859637669838952286847831235526582131 449576857262433441893039686426243410773226978028073189154411010 446823252716201052652272111660396665573092547110557853763466820 653109896526918620564769312570586356620185581007293606598764861 179104533488503461136576867532494416680396265797877185560845529 654126654085306143444318586769751456614068007002378776591344017 127494704205622305389945613140711270004078547332699390814546646 458807972708266830634328587856983052358089330657574067954571637 752542021149557615814002501262285941302164715509792592309907965 473761255176567513575178296664547791745011299614890304639947132 962107340437518957359614589019389713111790429782856475032031986 915140287080859904801094121472213179476477726224142548545403321 571853061422881375850430633217518297986622371721591607716692547 487389866549494501146540628433663937900397692656721463853067360 965712091807638327166416274888800786925602902284721040317211860 820419000422966171196377921337575114959501566049631862947265473 642523081770367515906735023507283540567040386743513622224771589 150495309844489333096340878076932599397805419341447377441842631 298608099888687413260472156951623965864573021631598193195167353 812974167729478672422924654366800980676928238280689964004824354 037014163149658979409243237896907069779422362508221688957383798 623001593776471651228935786015881617557829735233446042815126272 037343146531977774160319906655418763979293344195215413418994854 447345673831624993419131814809277771038638773431772075456545322 077709212019051660962804909263601975988281613323166636528619326 686336062735676303544776280350450777235547105859548702790814356 240145171806246436267945612753181340783303362542327839449753824 372058353114771199260638133467768796959703098339130771098704085 913374641442822772634659470474587847787201927715280731767907707 157213444730605700733492436931138350493163128404251219256517980 694113528013147013047816437885185290928545201165839341965621349 143415956258658655705526904965209858033850722426482939728584783 163057777560688876446248246857926039535277348030480290058760758 251047470916439613626760449256274204208320856611906254543372131 535958450687724602901618766795240616342522577195429162991930645 537799140373404328752628889639958794757291746426357455254079091 451357111369410911939325191076020825202618798531887705842972591 677813149699009019211697173727847684726860849003377024242916513 005005168323364350389517029893922334517220138128069650117844087 451960121228599371623130171144484640903890644954440061986907548 516026327505298349187407866808818338510228334508504860825039302 133219715518430635455007668282949304137765527939751754613953984 683393638304746119966538581538420568533862186725233402830871123 282789212507712629463229563989898935821167456270102183564622013 496715188190973038119800497340723961036854066431939509790190699 639552453005450580685501956730229219139339185680344903982059551 002263535361920419947455385938102343955449597783779023742161727 111723643435439478221818528624085140066604433258885698670543154 706965747458550332323342107301545940516553790686627333799585115 625784322988273723198987571415957811196358330059408730681216028 764962867446047746491599505497374256269010490377819868359381465 741268049256487985561453723478673303904688383436346553794986419 270563872931748723320837601123029911367938627089438799362016295 154133714248928307220126901475466847653576164773794675200490757 155527819653621323926406160136358155907422020203187277605277219 005561484255518792530343513984425322341576233610642506390497500 865627109535919465897514131034822769306247435363256916078154781 811528436679570611086153315044521274739245449454236828860613408 414863776700961207151249140430272538607648236341433462351897576 645216413767969031495019108575984423919862916421939949072362346 468441173940326591840443780513338945257423995082965912285085558 215725031071257012668302402929525220118726767562204154205161841 634847565169998116141010029960783869092916030288400269104140792 886215078424516709087000699282120660418371806535567252532567532 861291042487761825829765157959847035622262934860034158722980534 989650226291748788202734209222245339856264766914905562842503912 757710284027998066365825488926488025456610172967026640765590429 099456815065265305371829412703369313785178609040708667114965583 434347693385781711386455873678123014587687126603489139095620099 393610310291616152881384379099042317473363948045759314931405297 634757481193567091101377517210080315590248530906692037671922033 229094334676851422144773793937517034436619910403375111735471918 550464490263655128162288244625759163330391072253837421821408835 086573917715096828874782656995995744906617583441375223970968340 800535598491754173818839994469748676265516582765848358845314277 568790029095170283529716344562129640435231176006651012412006597 558512761785838292041974844236080071930457618932349229279650198 751872127267507981255470958904556357921221033346697499235630254 947802490114195212382815309114079073860251522742995818072471625 916685451333123948049470791191532673430282441860414263639548000 448002670496248201792896476697583183271314251702969234889627668 440323260927524960357996469256504936818360900323809293459588970 695365349406034021665443755890045632882250545255640564482465151 875471196218443965825337543885690941130315095261793780029741207 665147939425902989695946995565761218656196733786236256125216320 862869222103274889218654364802296780705765615144632046927906821 207388377814233562823608963208068222468012248261177185896381409 183903673672220888321513755600372798394004152970028783076670944 474560134556417254370906979396122571429894671543578468788614445 812314593571984922528471605049221242470141214780573455105008019 086996033027634787081081754501193071412233908663938339529425786 905076431006383519834389341596131854347546495569781038293097164 651438407007073604112373599843452251610507027056235266012764848 308407611830130527932054274628654036036745328651057065874882256 981579367897669742205750596834408697350201410206723585020072452 256326513410559240190274216248439140359989535394590944070469120 914093870012645600162374288021092764579310657922955249887275846 101264836999892256959688159205600101655256375678566722796619885 782794848855834397518744545512965634434803966420557982936804352 202770984294232533022576341807039476994159791594530069752148293 366555661567873640053666564165473217043903521329543529169

Now just reverse it. ;)

^^How's that?^^

O i c what u did thar.
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#39 eckboxes02
Member since 2007 • 226 Posts

If you can only use one combination a day, then i guess there's only one combination of five numbers.

per day, but how many day's do i got?

eckboxes02

the way that question is worded i think the answer is ( 1 )

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#40 Funky_Llama
Member since 2006 • 18428 Posts
[QUOTE="Acemaster27"]

[QUOTE="ChrisSpartan117"]Tell me what pie is when multiplied by itself.VacantPsalm

A square pi.

6.blahblahblahblahblah

Uhh, you mean 9.blablablablablabla.

Just what I thought :lol:
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#41 eckboxes02
Member since 2007 • 226 Posts
This question is missing some vital piece of information but I'm not sure what.
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#42 Kenny789
Member since 2006 • 10434 Posts
[QUOTE="Shad0ki11"][QUOTE="MoonMarvel"][QUOTE="edgewalker16"]

Hardest math problem ever?

Recite pi, in it's entirety, from memory...backwards!

Funky_Llama

-3.1415926535897932384626433832795028841971693993751058209749445 923078164062862089986280348253421170679821480865132823066470938 446095505822317253594081284811174502841027019385211055596446229 489549303819644288109756659334461284756482337867831652712019091 456485669234603486104543266482133936072602491412737245870066063 155881748815209209628292540917153643678925903600113305305488204 665213841469519415116094330572703657595919530921861173819326117 931051185480744623799627495673518857527248912279381830119491298 336733624406566430860213949463952247371907021798609437027705392 171762931767523846748184676694051320005681271452635608277857713 427577896091736371787214684409012249534301465495853710507922796 892589235420199561121290219608640344181598136297747713099605187 072113499999983729780499510597317328160963185950244594553469083 026425223082533446850352619311881710100031378387528865875332083 814206171776691473035982534904287554687311595628638823537875937 519577818577805321712268066130019278766111959092164201989380952 572010654858632788659361533818279682303019520353018529689957736 225994138912497217752834791315155748572424541506959508295331168 617278558890750983817546374649393192550604009277016711390098488 240128583616035637076601047101819429555961989467678374494482553 797747268471040475346462080466842590694912933136770289891521047 521620569660240580381501935112533824300355876402474964732639141 992726042699227967823547816360093417216412199245863150302861829 745557067498385054945885869269956909272107975093029553211653449 872027559602364806654991198818347977535663698074265425278625518 184175746728909777727938000816470600161452491921732172147723501 414419735685481613611573525521334757418494684385233239073941433 345477624168625189835694855620992192221842725502542568876717904 946016534668049886272327917860857843838279679766814541009538837 863609506800642251252051173929848960841284886269456042419652850 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496715188190973038119800497340723961036854066431939509790190699 639552453005450580685501956730229219139339185680344903982059551 002263535361920419947455385938102343955449597783779023742161727 111723643435439478221818528624085140066604433258885698670543154 706965747458550332323342107301545940516553790686627333799585115 625784322988273723198987571415957811196358330059408730681216028 764962867446047746491599505497374256269010490377819868359381465 741268049256487985561453723478673303904688383436346553794986419 270563872931748723320837601123029911367938627089438799362016295 154133714248928307220126901475466847653576164773794675200490757 155527819653621323926406160136358155907422020203187277605277219 005561484255518792530343513984425322341576233610642506390497500 865627109535919465897514131034822769306247435363256916078154781 811528436679570611086153315044521274739245449454236828860613408 414863776700961207151249140430272538607648236341433462351897576 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800535598491754173818839994469748676265516582765848358845314277 568790029095170283529716344562129640435231176006651012412006597 558512761785838292041974844236080071930457618932349229279650198 751872127267507981255470958904556357921221033346697499235630254 947802490114195212382815309114079073860251522742995818072471625 916685451333123948049470791191532673430282441860414263639548000 448002670496248201792896476697583183271314251702969234889627668 440323260927524960357996469256504936818360900323809293459588970 695365349406034021665443755890045632882250545255640564482465151 875471196218443965825337543885690941130315095261793780029741207 665147939425902989695946995565761218656196733786236256125216320 862869222103274889218654364802296780705765615144632046927906821 207388377814233562823608963208068222468012248261177185896381409 183903673672220888321513755600372798394004152970028783076670944 474560134556417254370906979396122571429894671543578468788614445 812314593571984922528471605049221242470141214780573455105008019 086996033027634787081081754501193071412233908663938339529425786 905076431006383519834389341596131854347546495569781038293097164 651438407007073604112373599843452251610507027056235266012764848 308407611830130527932054274628654036036745328651057065874882256 981579367897669742205750596834408697350201410206723585020072452 256326513410559240190274216248439140359989535394590944070469120 914093870012645600162374288021092764579310657922955249887275846 101264836999892256959688159205600101655256375678566722796619885 782794848855834397518744545512965634434803966420557982936804352 202770984294232533022576341807039476994159791594530069752148293 366555661567873640053666564165473217043903521329543529169

Now just reverse it. ;)

^^How's that?^^

O i c what u did thar.

Oh my gawd, wall of numbahs!!! :o Nothing will be able to break that! Except maybe... the Tsar Bomb? o_O
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#43 eckboxes02
Member since 2007 • 226 Posts

FACt: If in a computer there's 15 different programs,

I think the problem in this question is the relation between

statement - and you can only use 5 each day,

question - how many different combinations are there?

whats does the question relate to?

whats missing?

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#45 N0han
Member since 2007 • 982 Posts
The answer to your 'difficult' math problem is 15 NcR 5... type that in your calculator and youll have the answer.
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#46 eckboxes02
Member since 2007 • 226 Posts

The answer to your 'difficult' math problem is 15 NcR 5... type that in your calculator and youll have the answer.N0han

OK but the question isn't how many times you can make a combination of 5 separate numbers out of 15.

read the question again, it makes no sense.

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#47 Choga
Member since 2006 • 2377 Posts
5^15 = 3,051,758,125
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#48 Choga
Member since 2006 • 2377 Posts

[QUOTE="N0han"]The answer to your 'difficult' math problem is 15 NcR 5... type that in your calculator and youll have the answer.eckboxes02

OK but the question isn't how many times you can make a combination of 5 separate numbers out of 15.

read the question again, it makes no sense.

Yes the question is how many combinations of 5 programs out of 15 you can use per day.

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#49 eckboxes02
Member since 2007 • 226 Posts
[QUOTE="eckboxes02"]

[QUOTE="N0han"]The answer to your 'difficult' math problem is 15 NcR 5... type that in your calculator and youll have the answer.Choga

OK but the question isn't how many times you can make a combination of 5 separate numbers out of 15.

read the question again, it makes no sense.

Yes the question is how many combinations of 5 programs out of 15 you can use per day.

it says right in the quetion "and you can only use 5 each day"

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#50 Choga
Member since 2006 • 2377 Posts
[QUOTE="Choga"][QUOTE="eckboxes02"]

[QUOTE="N0han"]The answer to your 'difficult' math problem is 15 NcR 5... type that in your calculator and youll have the answer.eckboxes02

OK but the question isn't how many times you can make a combination of 5 separate numbers out of 15.

read the question again, it makes no sense.

Yes the question is how many combinations of 5 programs out of 15 you can use per day.

it says right in the quetion "and you can only use 5 each day"

Exactly. Read what I wrote again.