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2011 Powered Digits (Posted on 2011-03-25) Difficulty: 3 of 5
Find the first digit before and after the decimal point in the base ten expansion of (√2 + √3)2011.

For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
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re: spoiler- I don't know how you'd get this analytically | Comment 4 of 5 |
(In reply to spoiler- I don't know how you'd get this analytically by Charlie)

For those interested, the first 3000 digits are given as

11645859972873000139614914578761819986326263139755201897015671230060793394481132
08522121288724958958807534042183690658277875747360894972618952651816528108705031
45378237393596201204389137967347091577916147785838020125859059708307639956388635
28620431948232776899523683814557716177132308846495946390361118232369464467561737
70921127403988127989536094954623553590773823494489768522971844247408531428517928
74409727858340651360964349859003714692296874913435065346129992856686313455983824
74075415618189036600188696604050800940527635805123647234576826555488512300978062
25328817874433172212551805091233023062185007651452145375648158491780403692369353
39638114849338307359623105350206734917201808405358623269245431842422934457015650
11013910532993068465903597600281072199222475766288575962177330666683212884523643
09582141953473478039565997183839739193192315337577652995594388546936242766749142
08732977824103743156757737876536273564406069443750446838910164935047493661097593
453133656881166002424843496534218933931186.0363377139920859160260944803086607560
57604881623395217085144001767182933166824603277923522599079741482790203992366496
84283491593741350120752993833668654170944797195160523420946926989890601390955729
35844431883860541170836980738399950679933415212237944246865171901029660401366927
32566852931876246452487503918949156852347601747297067516348553066735243994506693
18907032046160528905121847871534375847229635308442287568056596391438504620776476
54207336075415407378622181066234905307493818563672261422833846852002939984565561
32552412648889233113667879288060598320293497764631754141921251658801565961160951
77908985856524301073036162942934496619960895709172886132036256042528328506574765
63685225370390247657783105931736737315936413957693588100604158153466146529541767
23217355852773735559107095685523755062639982051503336853262983187586150206365511
05414456754881069548668694857206491890298682982895697502045497678596624094685584
50383546093075143183263080919204060350014094889013096967788023187111331115532321
98933266927711799373758410958979584221901126610627587673210593425034696833583367
93454911723563006968488473168926456857372556996876920119228899717034332248060320
96394881456465107654879736061428724167424924766756557494012812193058341138966325
76232194826316047637805161716007648269335397599484783708863769667943180160777006
09122391804012092054341680849681121640383061586022671474795420213797579967414227
54032896257080801492804692220395201067329184633974547198389923769793218775101935
71966796296910642048614235706596094946244540723893651039306680437991098840063188
31893950723412259256735596503020811113553949553699971721822055587501218130402752
33486637997749710645364125222320908991156628650214604019536920135447742065763328
50487248247532219743635139705451750888837205389407386979160713821067370010846818
81677463172805552962707228918915034775392651806792645346691655642010450185331930
16202407387930833815300492585201345753854967534623850042890966691870711202247104
2442870693480714817162839168603704635445


  Posted by Charlie on 2011-03-25 22:22:32
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