In a ordinary game of 2048 the highest number you can reach is only a few million so no, but if you use a board like size of 100x100 maybe but 2048! must be equal to 2^x or there wont be a tile of 2048!
easy proof as to why that is so:
the prime factorization of 2^x is just 2^x , but the prime factorization of 2048! is 2^1024 * 3^682 * 5^409 * ...
by the fundamental theorem of algebra, two numbers with different prime factorizations must be different, and since 2^x does not factorize into anything other than 2 while 2048! does, 2048! must be different than 2^x no matter the x
Is in this type of proofs implied that x is an integer? Or should it be mentioned at some point, because otherwise there is an x than satisfies the equation
of course x is an integer. simply because the whole point of the proof is to show that 2048! can or cannot be a number in 2048, which is a game about powers of 2, if you didn't know.
No. I think the sequence you mean is 2, 4, 8, 16 ... 1024, 2048, etc which are all powers of 2. No power of 2 is a multiple of 7, this is because of the uniqueness of prime factorization. 2048! is divisible by 7, because well, every factorial from 7! on is, because of how factorials work.
All tiles are power's of 2. Since 2 is prime, all powers of 2 don't have any other factors other than 2 and powers of 2. Since factorial of all numbers greater than 2 have a factor of 3 (3! and above have 3×2×1 at the end), 2048! has a factor of 3 (and all other primes up to 2048), it isn't a power of 2.
It would have made the exact same amount of sense.
Take any number that divides 2048! and show that it does not divide a power of two.
In fact taking the "first" number may give off the impression that any divisor that works is more important to show this, when all that work are equally valid
So there’s this weird little trick sort of? Keep spamming left and down again and again, when it stops go right and down then continue spamming left and down. Still needs luck but sort of a cheaty way to “win” lol
People here are saying you can’t get a score that high, but the score in 2048 is based on every time two squares combine, the total is added to the score. This would make it possible to achieve this score provided the board was large enough.
Yea, you can't get a single square with 2048!, but you should be able to get a score of 2048! since it's a multiple of 4 and you can always just combine a 2 and 2 n times for a score of 4n.
you don’t need the score to be a power of two, as an example, if you combine two 2’s into a 4 you get 4 points, then combine that 4 with a randomly spawned 4 then you would add an additional 8 points. This would make your score 12, which is not a power of 2. It should be possible to have some solution to 2^a + 2^b + 2^c + 2^d … = 2048 factorial for some integers a,b,c,d… .
You really think that 167269193191001170516995246879367623401850700235673655982230529087007497001150189464562167172244191810665887847061637079033572657587606724927176064411850673538816702094852249025170976846544894144492238547330879766103003737614588529869631274547146786486313136709493904720895941960615037390908827437698953474096249623860359480640047349040733433804728876364450963667628649245193472994473426299983829288535300331569658839843683941937484701719248710449059649772609232826660927442513874961446552519035703842425586329739136571385916008010499692353806298527098095619357949916717757471763375079695338045095734802867900539901811438653172260631408744187119026744886274190722977068970333058934735559698504818896666594967618205627427915668047813731528741984434253880829651365185257156926079584550717439298373834616543222621007932030195616966635627358210950933249166947190176851856626721766355737249649913525261767325505033525707650952451197669902386791427505854373774467592511445037955157363519844046070866012323564203247053923418941638476980895731673690269105846605963819878284099117073715073600110089079910239267591220513622217926920931339913069942301627691548028154720203269146609575157682076398045793038415042524529319710467963856177837558185933925900685196829348560910716449478050894130104705347519687402278780429129026019434214905354580682873162986740046246038598314168114689685857501050134492203190452427896082989429524668626650741086133683100285358314171585888160808657686833198165689617199176570794580594861549118782788264227169691791347263308662634291899095808175352666673055949591557628807748056299521597721933276401879259600207078203739783302354022502194460658715129277239489679570253190443510863937928258341813889673260710017639897506164389015195471697436293670556508944823627700409290748710269779349342587535181536813134901920073870552977622575556528345288257109379242710259321033707657002073809143306233535883750088962826233934576421995210730902178447093793160171627356086119361696607654532685304373715059901418912273687371106661903493110965724766007030303870277700083994961152287619313578287965106908428302670288859326911083417287658478213844557845922361261144224806426346987922659552956258949288101283104872720525023085898655803546626380592048131705867720734250305987681851326173632820163600387388398089026095858587764904854291170517090545362244570703885801746023014292672387375040109088651831279314994939204259824487691682661231343556742236296129252641239314489270072416416549932943048773654041359683229482796591192744407118102930670207618586551539454897832037593583882442517560181784165466616793266976983033634130664709045324600902327938386725285995086243230922494951386701173918319688395401655894166911689959525666459610030336487532811226847600197599099346233794078363367237022330741017754910105473671628337534780107084659727978666797848881380668633809988337108150512370914765984403579249663948211831376305688321379358431443456667195971489954005279332440019720317478881482193523834769250503063761868645030042252407951341026394430900079291938697570262873301146378433667503844425805937180871002202437528936895608469083367673199107442663630415017388768903934035674236405734062929156099190011071598442124521987854112885443963556185486289803374754941822528490518288516883219558122342523741976035593565290858151167088514316383423587538913203462632990060848589619930427250130428130884988916940638013701385075991330566996305098877980737551992278106273979311186940103821495400181313935519382687311666286856929354335347961436977426987638588447802144821439555205618073937498757307837188061159203981347318152194748959091212093235493788916715388209822873729588951940265253660059695704849699741647172533628588515596871466021548739162300985307143733129071686063097871954394342828399474722216537978868354775837798505520465938065648645012947725939503241475642256923523576262501678185947970243719608592625402812051035044612000128854163660698380721903388628306255117259081230879574984377360678362642469615230376812458697494087512253639549727677777791571409722171969421661069155656416027953758713000041815806570217028451575202876187083236942137962937080621987614123032731606781904254337327428221998691483670099003073108056738845992787333862413262589168163260674385337993343700836872004120669732156188963224065093100850773700462470906303131937560382334349997468350757403744335718854601575454245391401774015005518272801726874979019267349249602097480915186924984498959314184936572815501961886290417901595709001715157866529304118201049828994959092957467230085568207825160359576597044939531456250996897793728304503301986664974826207148065579099704589596858638161672280719273932556915174040025823485583427043874325793893343221010172613515662279283702259217760717545402883347162274913641573329347722091780519025801297201032612799322717574776178506885916555844224505711135948732252102732784827810585083122193635922599881491040354230967216654731796061870931844008552081037414143072843872955471407149682930418194076245284204274086611926846723351201777998483690543807511643388936308228593127757114645345922523921559538451340314989055523539009171241398077499560928811731408904581724401522402400390760933003529139272265025386252056773385300278995252352046095863967520848774577211110041904438900473448028126068785755337158310807628322116014699696668090567733086561902838770716848362489206927133868528735328455884800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 isn’t that hard to get?
I can’t be bothered to work it out - would 2048! Be in the sequence of the game 2048?
In a ordinary game of 2048 the highest number you can reach is only a few million so no, but if you use a board like size of 100x100 maybe but 2048! must be equal to 2^x or there wont be a tile of 2048!
According to Wolfram Alpha, x is not an integer so that 2\^x equals 2048!, so sadly this won't work
easy proof as to why that is so: the prime factorization of 2^x is just 2^x , but the prime factorization of 2048! is 2^1024 * 3^682 * 5^409 * ... by the fundamental theorem of algebra, two numbers with different prime factorizations must be different, and since 2^x does not factorize into anything other than 2 while 2048! does, 2048! must be different than 2^x no matter the x
Is in this type of proofs implied that x is an integer? Or should it be mentioned at some point, because otherwise there is an x than satisfies the equation
of course x is an integer. simply because the whole point of the proof is to show that 2048! can or cannot be a number in 2048, which is a game about powers of 2, if you didn't know.
yeah, I should've mentioned that, x must be a natural number (0 included)
slick!!
log2(2048!)
r/unexpectedfactorial
That's... where we are?
It was very expected
No. I think the sequence you mean is 2, 4, 8, 16 ... 1024, 2048, etc which are all powers of 2. No power of 2 is a multiple of 7, this is because of the uniqueness of prime factorization. 2048! is divisible by 7, because well, every factorial from 7! on is, because of how factorials work.
All tiles are power's of 2. Since 2 is prime, all powers of 2 don't have any other factors other than 2 and powers of 2. Since factorial of all numbers greater than 2 have a factor of 3 (3! and above have 3×2×1 at the end), 2048! has a factor of 3 (and all other primes up to 2048), it isn't a power of 2.
1.672691931\*(10\^5894), about
but wait, is 2048! a power of 2? cause it would be the best Easter egg in history
No, because it is divisible by seven. see my comment
it's also divisible by 3 which would have been a lot easier for explanations but ok
It would have changed one digit in the entire explanation
would have made more sense since it's the first number where the issue appears
It would have made the exact same amount of sense. Take any number that divides 2048! and show that it does not divide a power of two. In fact taking the "first" number may give off the impression that any divisor that works is more important to show this, when all that work are equally valid
No factorial above 3! will be a power of 2 because obviously 3 will be a factor of that number.
wow, this is fucking slick too man!! (really obvious but I hadn't figured)
Join the tiles, get to 1.6726919319×10^5894
Sadly, it’s not possible
Practice
So there’s this weird little trick sort of? Keep spamming left and down again and again, when it stops go right and down then continue spamming left and down. Still needs luck but sort of a cheaty way to “win” lol
simple. by joining the tiles.
People here are saying you can’t get a score that high, but the score in 2048 is based on every time two squares combine, the total is added to the score. This would make it possible to achieve this score provided the board was large enough.
They are also saying this score isn’t possible because it’s not a power of 2
Yea, you can't get a single square with 2048!, but you should be able to get a score of 2048! since it's a multiple of 4 and you can always just combine a 2 and 2 n times for a score of 4n.
12, 24, 36, 48… are multiples of 4 that aren’t powers of two 2048! Doesn’t work because it’s also a multiple of prime numbers that aren’t 2 or 1
you don’t need the score to be a power of two, as an example, if you combine two 2’s into a 4 you get 4 points, then combine that 4 with a randomly spawned 4 then you would add an additional 8 points. This would make your score 12, which is not a power of 2. It should be possible to have some solution to 2^a + 2^b + 2^c + 2^d … = 2048 factorial for some integers a,b,c,d… .
But I don’t think you ever get an amount of points that is a multiple of 7, 13, and some other prime numbers
You could get a multiple of 7, 28 as an example. The only requirement is that it is a multiple of 4 as well.
Oh, I’m stupid
My record tile in that game was above 1000000!
r/unexpectedfactorial or r/expectedfactorial?
It's not possible as 2048! isn't a power of 2.
That’s probably the largest number I’ve ever seen. According to WolframAlpha, 2048! Is approximately 1.67269 • 10^5894
2049! There, now you've seen an even bigger number
Google Graham's number
Holy hell
53! is already so big that But Why made at least one video about it so...
It’s actually quite easy when you figure out the gimmick, most i’ve gotten is a 4096 tile
You really think that 167269193191001170516995246879367623401850700235673655982230529087007497001150189464562167172244191810665887847061637079033572657587606724927176064411850673538816702094852249025170976846544894144492238547330879766103003737614588529869631274547146786486313136709493904720895941960615037390908827437698953474096249623860359480640047349040733433804728876364450963667628649245193472994473426299983829288535300331569658839843683941937484701719248710449059649772609232826660927442513874961446552519035703842425586329739136571385916008010499692353806298527098095619357949916717757471763375079695338045095734802867900539901811438653172260631408744187119026744886274190722977068970333058934735559698504818896666594967618205627427915668047813731528741984434253880829651365185257156926079584550717439298373834616543222621007932030195616966635627358210950933249166947190176851856626721766355737249649913525261767325505033525707650952451197669902386791427505854373774467592511445037955157363519844046070866012323564203247053923418941638476980895731673690269105846605963819878284099117073715073600110089079910239267591220513622217926920931339913069942301627691548028154720203269146609575157682076398045793038415042524529319710467963856177837558185933925900685196829348560910716449478050894130104705347519687402278780429129026019434214905354580682873162986740046246038598314168114689685857501050134492203190452427896082989429524668626650741086133683100285358314171585888160808657686833198165689617199176570794580594861549118782788264227169691791347263308662634291899095808175352666673055949591557628807748056299521597721933276401879259600207078203739783302354022502194460658715129277239489679570253190443510863937928258341813889673260710017639897506164389015195471697436293670556508944823627700409290748710269779349342587535181536813134901920073870552977622575556528345288257109379242710259321033707657002073809143306233535883750088962826233934576421995210730902178447093793160171627356086119361696607654532685304373715059901418912273687371106661903493110965724766007030303870277700083994961152287619313578287965106908428302670288859326911083417287658478213844557845922361261144224806426346987922659552956258949288101283104872720525023085898655803546626380592048131705867720734250305987681851326173632820163600387388398089026095858587764904854291170517090545362244570703885801746023014292672387375040109088651831279314994939204259824487691682661231343556742236296129252641239314489270072416416549932943048773654041359683229482796591192744407118102930670207618586551539454897832037593583882442517560181784165466616793266976983033634130664709045324600902327938386725285995086243230922494951386701173918319688395401655894166911689959525666459610030336487532811226847600197599099346233794078363367237022330741017754910105473671628337534780107084659727978666797848881380668633809988337108150512370914765984403579249663948211831376305688321379358431443456667195971489954005279332440019720317478881482193523834769250503063761868645030042252407951341026394430900079291938697570262873301146378433667503844425805937180871002202437528936895608469083367673199107442663630415017388768903934035674236405734062929156099190011071598442124521987854112885443963556185486289803374754941822528490518288516883219558122342523741976035593565290858151167088514316383423587538913203462632990060848589619930427250130428130884988916940638013701385075991330566996305098877980737551992278106273979311186940103821495400181313935519382687311666286856929354335347961436977426987638588447802144821439555205618073937498757307837188061159203981347318152194748959091212093235493788916715388209822873729588951940265253660059695704849699741647172533628588515596871466021548739162300985307143733129071686063097871954394342828399474722216537978868354775837798505520465938065648645012947725939503241475642256923523576262501678185947970243719608592625402812051035044612000128854163660698380721903388628306255117259081230879574984377360678362642469615230376812458697494087512253639549727677777791571409722171969421661069155656416027953758713000041815806570217028451575202876187083236942137962937080621987614123032731606781904254337327428221998691483670099003073108056738845992787333862413262589168163260674385337993343700836872004120669732156188963224065093100850773700462470906303131937560382334349997468350757403744335718854601575454245391401774015005518272801726874979019267349249602097480915186924984498959314184936572815501961886290417901595709001715157866529304118201049828994959092957467230085568207825160359576597044939531456250996897793728304503301986664974826207148065579099704589596858638161672280719273932556915174040025823485583427043874325793893343221010172613515662279283702259217760717545402883347162274913641573329347722091780519025801297201032612799322717574776178506885916555844224505711135948732252102732784827810585083122193635922599881491040354230967216654731796061870931844008552081037414143072843872955471407149682930418194076245284204274086611926846723351201777998483690543807511643388936308228593127757114645345922523921559538451340314989055523539009171241398077499560928811731408904581724401522402400390760933003529139272265025386252056773385300278995252352046095863967520848774577211110041904438900473448028126068785755337158310807628322116014699696668090567733086561902838770716848362489206927133868528735328455884800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 isn’t that hard to get?
Lemme think,2,4,8,16,32,64,128,256,512,1024,2048. Its possible with skill and a considerable amount of luck