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document.write( "Here is the correct solution, which is 626.\r\n" );
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document.write( "Break them down into 4 types: AAAB-type, AABB-type, AABC-type, and ABCD-type.\r\n" );
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document.write( "Each distinguishable 4-letter arrangement that can be made from the letters in\r\n" );
document.write( "the word REPRESENT can be made by replacing the letters A,B,C,D in some\r\n" );
document.write( "distinguishable arrangement of one of these AAAB, AABB, AABC, or ABCD, by\r\n" );
document.write( "letters from the set {R,E,P,S,N,T}\r\n" );
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document.write( "Case 1. AAAB. There are 4!/3!=4 distinguishable arrangements of AAAB.\r\n" );
document.write( "For each of those 4 arrangements of AAAB, we can replace the A 1 way (as E),\r\n" );
document.write( "and we can then replace the B by any of the other 5 letters. So there are 4*1*5=20\r\n" );
document.write( "distinguishable arrangements of the AAAB-type.\r\n" );
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document.write( "Case 2. AABB. There are 4!/(2!2!)=6 distinguishable arrangements of AABB.\r\n" );
document.write( "For each of those 6 distinguishable arrangements of AABB, there is only one way\r\n" );
document.write( "to choose a combination of letters to replace the combination {A,B} by and that\r\n" );
document.write( "one combination is the combination {R,E}. So there are 6*1=6 distinguishable\r\n" );
document.write( "arrangements of the AABB-type.\r\n" );
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document.write( "Case 3. AABC. There are 4!/2!=12 distinguishable arrangements of AABC.\r\n" );
document.write( "For each of those 12 arrangements of AABC, we can replace the A 2 ways (R or E),\r\n" );
document.write( "and we can then replace the B by any of the other 5 unselected letters. Then we\r\n" );
document.write( "can replace the C by any of the remaining 4 unselected letters. So there are\r\n" );
document.write( "12*5*4=240 distinguishable arrangements of the AABC-type.\r\n" );
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document.write( "Case 4. ABCD. There are 4!=24 arrangements of ABCD, all distinguishable. For\r\n" );
document.write( "each of these 24, we can replace A,B,C,D with a permutation of these 6 things\r\n" );
document.write( "{R,E,P,S,N,T} taken 4 at a time. That's 6P4 = 6*5*4*3 = 360 distinguishable\r\n" );
document.write( " arrangements of the ABCD-type.\r\n" );
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document.write( "That gives a total of 20+6+240+360 = 626.\r\n" );
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document.write( "Below are all 626 distinguishable 4-letter arrangements from REPRESENT, \r\n" );
document.write( "computer-generated. 48 full rows of 13 each. That's 48*13=624 plus the\r\n" );
document.write( "49th row only has 2. \r\n" );
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document.write( "REPR, REPE, REPS, REPN, REPT, RERP, RERE, RERS, RERN, RERT, REEP, REER, REES,\r\n" );
document.write( "REEE, REEN, REET, RESP, RESR, RESE, RESN, REST, RENP, RENR, RENE, RENS, RENT,\r\n" );
document.write( "RETP, RETR, RETE, RETS, RETN, RPER, RPEE, RPES, RPEN, RPET, RPRE, RPRS, RPRN,\r\n" );
document.write( "RPRT, RPSE, RPSR, RPSN, RPST, RPNE, RPNR, RPNS, RPNT, RPTE, RPTR, RPTS, RPTN,\r\n" );
document.write( "RREP, RREE, RRES, RREN, RRET, RRPE, RRPS, RRPN, RRPT, RRSE, RRSP, RRSN, RRST,\r\n" );
document.write( "RRNE, RRNP, RRNS, RRNT, RRTE, RRTP, RRTS, RRTN, RSEP, RSER, RSEE, RSEN, RSET,\r\n" );
document.write( "RSPE, RSPR, RSPN, RSPT, RSRE, RSRP, RSRN, RSRT, RSNE, RSNP, RSNR, RSNT, RSTE,\r\n" );
document.write( "RSTP, RSTR, RSTN, RNEP, RNER, RNEE, RNES, RNET, RNPE, RNPR, RNPS, RNPT, RNRE,\r\n" );
document.write( "RNRP, RNRS, RNRT, RNSE, RNSP, RNSR, RNST, RNTE, RNTP, RNTR, RNTS, RTEP, RTER,\r\n" );
document.write( "RTEE, RTES, RTEN, RTPE, RTPR, RTPS, RTPN, RTRE, RTRP, RTRS, RTRN, RTSE, RTSP,\r\n" );
document.write( "RTSR, RTSN, RTNE, RTNP, RTNR, RTNS, ERPR, ERPE, ERPS, ERPN, ERPT, ERRP, ERRE,\r\n" );
document.write( "ERRS, ERRN, ERRT, EREP, ERER, ERES, EREE, EREN, ERET, ERSP, ERSR, ERSE, ERSN,\r\n" );
document.write( "ERST, ERNP, ERNR, ERNE, ERNS, ERNT, ERTP, ERTR, ERTE, ERTS, ERTN, EPRR, EPRE,\r\n" );
document.write( "EPRS, EPRN, EPRT, EPER, EPES, EPEE, EPEN, EPET, EPSR, EPSE, EPSN, EPST, EPNR,\r\n" );
document.write( "EPNE, EPNS, EPNT, EPTR, EPTE, EPTS, EPTN, EERP, EERR, EERS, EERE, EERN, EERT,\r\n" );
document.write( "EEPR, EEPS, EEPE, EEPN, EEPT, EESR, EESP, EESE, EESN, EEST, EEER, EEEP, EEES,\r\n" );
document.write( "EEEN, EEET, EENR, EENP, EENS, EENE, EENT, EETR, EETP, EETS, EETE, EETN, ESRP,\r\n" );
document.write( "ESRR, ESRE, ESRN, ESRT, ESPR, ESPE, ESPN, ESPT, ESER, ESEP, ESEE, ESEN, ESET,\r\n" );
document.write( "ESNR, ESNP, ESNE, ESNT, ESTR, ESTP, ESTE, ESTN, ENRP, ENRR, ENRE, ENRS, ENRT,\r\n" );
document.write( "ENPR, ENPE, ENPS, ENPT, ENER, ENEP, ENES, ENEE, ENET, ENSR, ENSP, ENSE, ENST,\r\n" );
document.write( "ENTR, ENTP, ENTE, ENTS, ETRP, ETRR, ETRE, ETRS, ETRN, ETPR, ETPE, ETPS, ETPN,\r\n" );
document.write( "ETER, ETEP, ETES, ETEE, ETEN, ETSR, ETSP, ETSE, ETSN, ETNR, ETNP, ETNE, ETNS,\r\n" );
document.write( "PRER, PREE, PRES, PREN, PRET, PRRE, PRRS, PRRN, PRRT, PRSE, PRSR, PRSN, PRST,\r\n" );
document.write( "PRNE, PRNR, PRNS, PRNT, PRTE, PRTR, PRTS, PRTN, PERR, PERE, PERS, PERN, PERT,\r\n" );
document.write( "PEER, PEES, PEEE, PEEN, PEET, PESR, PESE, PESN, PEST, PENR, PENE, PENS, PENT,\r\n" );
document.write( "PETR, PETE, PETS, PETN, PSRE, PSRR, PSRN, PSRT, PSER, PSEE, PSEN, PSET, PSNR,\r\n" );
document.write( "PSNE, PSNT, PSTR, PSTE, PSTN, PNRE, PNRR, PNRS, PNRT, PNER, PNEE, PNES, PNET,\r\n" );
document.write( "PNSR, PNSE, PNST, PNTR, PNTE, PNTS, PTRE, PTRR, PTRS, PTRN, PTER, PTEE, PTES,\r\n" );
document.write( "PTEN, PTSR, PTSE, PTSN, PTNR, PTNE, PTNS, SREP, SRER, SREE, SREN, SRET, SRPE,\r\n" );
document.write( "SRPR, SRPN, SRPT, SRRE, SRRP, SRRN, SRRT, SRNE, SRNP, SRNR, SRNT, SRTE, SRTP,\r\n" );
document.write( "SRTR, SRTN, SERP, SERR, SERE, SERN, SERT, SEPR, SEPE, SEPN, SEPT, SEER, SEEP,\r\n" );
document.write( "SEEE, SEEN, SEET, SENR, SENP, SENE, SENT, SETR, SETP, SETE, SETN, SPRE, SPRR,\r\n" );
document.write( "SPRN, SPRT, SPER, SPEE, SPEN, SPET, SPNR, SPNE, SPNT, SPTR, SPTE, SPTN, SNRE,\r\n" );
document.write( "SNRP, SNRR, SNRT, SNER, SNEP, SNEE, SNET, SNPR, SNPE, SNPT, SNTR, SNTE, SNTP,\r\n" );
document.write( "STRE, STRP, STRR, STRN, STER, STEP, STEE, STEN, STPR, STPE, STPN, STNR, STNE,\r\n" );
document.write( "STNP, NREP, NRER, NREE, NRES, NRET, NRPE, NRPR, NRPS, NRPT, NRRE, NRRP, NRRS,\r\n" );
document.write( "NRRT, NRSE, NRSP, NRSR, NRST, NRTE, NRTP, NRTR, NRTS, NERP, NERR, NERE, NERS,\r\n" );
document.write( "NERT, NEPR, NEPE, NEPS, NEPT, NEER, NEEP, NEES, NEEE, NEET, NESR, NESP, NESE,\r\n" );
document.write( "NEST, NETR, NETP, NETE, NETS, NPRE, NPRR, NPRS, NPRT, NPER, NPEE, NPES, NPET,\r\n" );
document.write( "NPSR, NPSE, NPST, NPTR, NPTE, NPTS, NSRE, NSRP, NSRR, NSRT, NSER, NSEP, NSEE,\r\n" );
document.write( "NSET, NSPR, NSPE, NSPT, NSTR, NSTE, NSTP, NTRE, NTRP, NTRR, NTRS, NTER, NTEP,\r\n" );
document.write( "NTEE, NTES, NTPR, NTPE, NTPS, NTSR, NTSE, NTSP, TREP, TRER, TREE, TRES, TREN,\r\n" );
document.write( "TRPE, TRPR, TRPS, TRPN, TRRE, TRRP, TRRS, TRRN, TRSE, TRSP, TRSR, TRSN, TRNE,\r\n" );
document.write( "TRNP, TRNR, TRNS, TERP, TERR, TERE, TERS, TERN, TEPR, TEPE, TEPS, TEPN, TEER,\r\n" );
document.write( "TEEP, TEES, TEEE, TEEN, TESR, TESP, TESE, TESN, TENR, TENP, TENE, TENS, TPRE,\r\n" );
document.write( "TPRR, TPRS, TPRN, TPER, TPEE, TPES, TPEN, TPSR, TPSE, TPSN, TPNR, TPNE, TPNS,\r\n" );
document.write( "TSRE, TSRP, TSRR, TSRN, TSER, TSEP, TSEE, TSEN, TSPR, TSPE, TSPN, TSNR, TSNE,\r\n" );
document.write( "TSNP, TNRE, TNRP, TNRR, TNRS, TNER, TNEP, TNEE, TNES, TNPR, TNPE, TNPS, TNSR,\r\n" );
document.write( "TNSE, TNSP\r\n" );
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document.write( "Edwin\n" ); document.write( " \n" ); document.write( "