Reading right to left, determine the 2500th digit of 10000!

*** For an extra challenge, solve this puzzle without the aid of a computer program.

  5   F=1
 10   for I=1 to 10000
 15   if log(F)>5900 then F=F/100
 20   F=F*I/1
 25   if log(F)>5900 then F=F/100
 30   next
 40   print F

produces

 2846259680917054518906413212119868890148051401702799230794179994274411340003764
44377299078675778477581588406214231752883004233994015351873905242116138271617481
98241998275924182892597878981242531205946599625986706560161572036032397926328736
71705574197596209947972034615369811989709261127750048419884541047554464244213657
33030767036288258035489674611170973695786036701910715127305872810411586405612811
65385325968425825995584688146430425589836649317059251717204276597407446133400054
19405246230343686915405940406622782824837151203832217864462718382292389963899282
72218797024593876938030946273322925705554596900278752822425443480211275590191694
25429028916907219097083690539873747452483372899521802363282741217040268086769210
45155584056717255537201585213282903427998981844931361064038148930449962159999935
96708929801903369984844046654192362584249471631789611920412331082686510713545168
45540936033009607210346944377982349430780626069422302681885227592057029230843126
18849760656074258627944882715595683153344053442544664841689458042570946167361318
76052349822863264529215294234798706033442907371586884991789325806914831688542519
56006172372636323974420786924642956012306288720122652952964091508301336630982733
80635397290150658182257429547589439976511386554120812578868370423920876448476156
90012648892715907063064096616280387840444851916437908071861123706221334154150659
91843875961023926713276546986163657706626438638029848051952769536195259240930908
61447190739076858575593478698172073437209310482547562856777769408156407496227525
49933841128092896375169902198704924056175317863469397980246197370790418683299310
16554150742308393176878366923694849025999607729684293977427536263119825416681531
89176323483919082100014717893218422780513518173492190114624687576983537344145601
31226152213911787596883673640872079370029920382791980387023720780391403123689976
08152840306051116709484722224870389199993442071395836983063962232079115624044250
80891991431983712044559834404755675948921210149815245454359428541439084356441998
42248554785321636240300984428553318292531542065512370797058163934602962476970103
88742206441536626733715428700789122749340684336442889847100840641600093623935261
24803797529334392876439831639031277645072247926785170082666959838952615075900734
92151975926591927088732025940663821188019888547482660483422564577057439731222597
00671936061763513579529821794290797705327283267501488024443528681645026165662837
54651900617187344226043891929850607151539003110668472736013581670643786175675743
91843764796581361005996386895523346487817461432435732248643267984819814584327030
35895.5084205347884256662

The first line contains the first 79 digits of the factorial sought and each successive line contains then next 80 digits. Now, 2500 = 31*80 + 20 = 30*80 + 79 + 21, so the character sought should be the 21st digit on the 32nd line: it's a 9, the middle of ...0059963....

The number shown of course is not the complete factorial as it has been divided by 100 at various times.  The program doesn't count how many times. The real factorial has 35660 digits.

Posted by Charlie on 2011-10-01 18:32:17