MATEMANIJA

Ovako glasi zadatak:
Kako glasi [inlmath]197.[/inlmath] kombinacija [inlmath]5.[/inlmath] klase prvih [inlmath]12[/inlmath] slova azbuke uzimajuci te kombinacije u leksigrafskom poretku?
Posmatraju se elementi: [inlmath]a,b,c,d,e,f,g,h,i,j,k,l[/inlmath]
Ako krenemo ovako : [inlmath]ab|\_\:\_\:\_|\;{10\choose3}=120[/inlmath]
[inlmath]ac|\_\:\_\:\_|\;{9\choose3}=84\quad120+84=204[/inlmath], dakle u tom je "intervalu".

[inlmath]acd|\_\:\_|\;{8\choose2}=28\quad120+28=148[/inlmath]
[inlmath]ace|\_\:\_|\;{7\choose2}=21\quad148+21=169[/inlmath]
[inlmath]acf|\_\:\_|\;{6\choose2}=15\quad169+15=184[/inlmath]
[inlmath]acg|\_\:\_|\;{5\choose2}=10\quad184+10=194[/inlmath]
[inlmath]achij=195[/inlmath]
[inlmath]achik=196[/inlmath]
[inlmath]\enclose{box}{achil}=197.[/inlmath] trazena kombinacija, stvarno ne vidim kako moze da resenja budu sledeca
Da, resenja, jer za ovaj zadatak koji ima isti tekst, imam dva razlicita resenja iz dve razlicite zbirke, jedno iz 1980. godine kaze: [inlmath]acghk[/inlmath], a drugo iz 2011. godine [inlmath]aeghk[/inlmath].
Ko god protumaci/proveri ovaj zadatak bicu zahvalan.

JohnLocke je napisao:Kako glasi [inlmath]197.[/inlmath] kombinacija [inlmath]5.[/inlmath] klase prvih [inlmath]12[/inlmath] slova azbuke uzimajuci te kombinacije u leksigrafskom poretku?

Prvih [inlmath]12[/inlmath] slova azbuke su [inlmath]a,b,v,g,d,đ,e,ž,z,i,j,k[/inlmath]. Međutim, u svim ponuđenim rešenjima figuriše slovo [inlmath]h[/inlmath], koje je tek pri kraju azbuke.
Pretpostaviću da su u pitanju prvih [inlmath]12[/inlmath] slova abecede.

U tom slučaju, potvrđujem tačnost tvog rešenja, a nije me mrzelo čak i da proverim tabelarno (nije bilo toliko posla kao što na prvi pogled izgleda, 80% je copy/paste):
[dispmath]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline & +1 & +2 & +3 & +4 & +5 & +6 & +7 & +8 & +9 & +10\\ \hline 0 & \mathtt{abcde} & \mathtt{abcdf} & \mathtt{abcdg} & \mathtt{abcdh} & \mathtt{abcdi} & \mathtt{abcdj} & \mathtt{abcdk} & \mathtt{abcdl} & \mathtt{abcef} & \mathtt{abceg}\\ \hline 10 & \mathtt{abceh} & \mathtt{abcei} & \mathtt{abcej} & \mathtt{abcek} & \mathtt{abcel} & \mathtt{abcfg} & \mathtt{abcfh} & \mathtt{abcfi} & \mathtt{abcfj} & \mathtt{abcfk}\\ \hline 20 & \mathtt{abcfl} & \mathtt{abcgh} & \mathtt{abcgi} & \mathtt{abcgj} & \mathtt{abcgk} & \mathtt{abcgl} & \mathtt{abchi} & \mathtt{abchj} & \mathtt{abchk} & \mathtt{abchl}\\ \hline 30 & \mathtt{abcij} & \mathtt{abcik} & \mathtt{abcil} & \mathtt{abcjk} & \mathtt{abcjl} & \mathtt{abckl} & \mathtt{abdef} & \mathtt{abdeg} & \mathtt{abdeh} & \mathtt{abdei}\\ \hline 40 & \mathtt{abdej} & \mathtt{abdek} & \mathtt{abdel} & \mathtt{abdfg} & \mathtt{abdfh} & \mathtt{abdfi} & \mathtt{abdfj} & \mathtt{abdfk} & \mathtt{abdfl} & \mathtt{abdgh}\\ \hline 50 & \mathtt{abdgi} & \mathtt{abdgj} & \mathtt{abdgk} & \mathtt{abdgl} & \mathtt{abdhi} & \mathtt{abdhj} & \mathtt{abdhk} & \mathtt{abdhl} & \mathtt{abdij} & \mathtt{abdik}\\ \hline 60 & \mathtt{abdil} & \mathtt{abdjk} & \mathtt{abdjl} & \mathtt{abdkl} & \mathtt{abefg} & \mathtt{abefh} & \mathtt{abefi} & \mathtt{abefj} & \mathtt{abefk} & \mathtt{abefl}\\ \hline 70 & \mathtt{abegh} & \mathtt{abegi} & \mathtt{abegj} & \mathtt{abegk} & \mathtt{abegl} & \mathtt{abehi} & \mathtt{abehj} & \mathtt{abehk} & \mathtt{abehl} & \mathtt{abeij}\\ \hline 80 & \mathtt{abeik} & \mathtt{abeil} & \mathtt{abejk} & \mathtt{abejl} & \mathtt{abekl} & \mathtt{abfgh} & \mathtt{abfgi} & \mathtt{abfgj} & \mathtt{abfgk} & \mathtt{abfgl}\\ \hline 90 & \mathtt{abfhi} & \mathtt{abfhj} & \mathtt{abfhk} & \mathtt{abfhl} & \mathtt{abfij} & \mathtt{abfik} & \mathtt{abfil} & \mathtt{abfjk} & \mathtt{abfjl} & \mathtt{abfkl}\\ \hline 100 & \mathtt{abghi} & \mathtt{abghj} & \mathtt{abghk} & \mathtt{abghl} & \mathtt{abgij} & \mathtt{abgik} & \mathtt{abgil} & \mathtt{abgjk} & \mathtt{abgjl} & \mathtt{abgkl}\\ \hline 110 & \mathtt{abhij} & \mathtt{abhik} & \mathtt{abhil} & \mathtt{abhjk} & \mathtt{abhjl} & \mathtt{abhkl} & \mathtt{abijk} & \mathtt{abijl} & \mathtt{abikl} & \mathtt{abjkl}\\ \hline 120 & \mathtt{acdef} & \mathtt{acdeg} & \mathtt{acdeh} & \mathtt{acdei} & \mathtt{acdej} & \mathtt{acdek} & \mathtt{acdel} & \mathtt{acdfg} & \mathtt{acdfh} & \mathtt{acdfi}\\ \hline 130 & \mathtt{acdfj} & \mathtt{acdfk} & \mathtt{acdfl} & \mathtt{acdgh} & \mathtt{acdgi} & \mathtt{acdgj} & \mathtt{acdgk} & \mathtt{acdgl} & \mathtt{acdhi} & \mathtt{acdhj}\\ \hline 140 & \mathtt{acdhk} & \mathtt{acdhl} & \mathtt{acdij} & \mathtt{acdik} & \mathtt{acdil} & \mathtt{acdjk} & \mathtt{acdjl} & \mathtt{acdkl} & \mathtt{acefg} & \mathtt{acefh}\\ \hline 150 & \mathtt{acefi} & \mathtt{acefj} & \mathtt{acefk} & \mathtt{acefl} & \mathtt{acegh} & \mathtt{acegi} & \mathtt{acegj} & \mathtt{acegk} & \mathtt{acegl} & \mathtt{acehi}\\ \hline 160 & \mathtt{acehj} & \mathtt{acehk} & \mathtt{acehl} & \mathtt{aceij} & \mathtt{aceik} & \mathtt{aceil} & \mathtt{acejk} & \mathtt{acejl} & \mathtt{acekl} & \mathtt{acfgh}\\ \hline 170 & \mathtt{acfgi} & \mathtt{acfgj} & \mathtt{acfgk} & \mathtt{acfgl} & \mathtt{acfhi} & \mathtt{acfhj} & \mathtt{acfhk} & \mathtt{acfhl} & \mathtt{acfij} & \mathtt{acfik}\\ \hline 180 & \mathtt{acfil} & \mathtt{acfjk} & \mathtt{acfjl} & \mathtt{acfkl} & \mathtt{acghi} & \mathtt{acghj} & \mathtt{acghk} & \mathtt{acghl} & \mathtt{acgij} & \mathtt{acgik}\\ \hline 190 & \mathtt{acgil} & \mathtt{acgjk} & \mathtt{acgjl} & \mathtt{acgkl} & \mathtt{achij} & \mathtt{achik} & \color{red}\mathtt{achil} & \mathtt{achjk} & \mathtt{achjl} & \mathtt{achkl}\\ \hline 200 & \mathtt{acijk} & \mathtt{acijl} & \mathtt{acikl} & \mathtt{acjkl} & \mathtt{adefg} & \mathtt{adefh} & \mathtt{adefi} & \mathtt{adefj} & \mathtt{adefk} & \mathtt{adefl}\\ \hline \end{array}[/dispmath]
[inlmath]acghk[/inlmath], rešenje koje je navedeno u zbirci iz 1980. godine, predstavljalo bi [inlmath]187.[/inlmath] leksikografsku kombinaciju. Proveri da nisi možda pogrešno pročitao, da ne piše možda [inlmath]187.[/inlmath] umesto [inlmath]197.[/inlmath] kombinacija.

Istina, sve ovo je uz jednu malu ogradu – različiti autori različito tumače redni broj početne leksikografske kombinacije (u ovom slučaju [inlmath]abcde[/inlmath]). Jedni smatraju da bi to bila prva leksikografska kombinacija (u tom slučaju rešenje bi bilo, kao što si i napisao, [inlmath]achil[/inlmath]), dok drugi autori početnu leksikografsku kombinaciju označavaju kao nultu (u tom slučaju [inlmath]197.[/inlmath] kombinacija bi bila prva nakon [inlmath]achil[/inlmath], tj. [inlmath]achjk[/inlmath]).
(O toj nedoslednosti (nažalost, ne jedinoj u matematici) govorili smo u ovoj temi.)

Da da pise u tekstu azbuke, i to u izdanju iz [inlmath]'80[/inlmath]te a u izdanju iz [inlmath]2011.[/inlmath] je korigovano na abecedu (primecena greska ocigledno).
Moguce da su zeleli da postave zadatak za [inlmath]187.[/inlmath] kombinaciju, mozda neka greska u kucanju, ne znam, inace u pitanju je [inlmath]197.[/inlmath] provereno
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