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KIRKMANOV PROBLEM O UĈENICAMA
KIRKMAN'S SCHOOLGIRL PROBLEM

Uĉenik : NIKOLINA MARKOVIĆ I razred Gimnazija u Lazarevcu
Mentor : VESNA RAJŠIĆ, profesor matematike Elektrotehniĉka škola „Nikola Tesla”

REZIME

Kirkmanov problem o uĉenicama intezivno je izuĉavan u 19. veku, ali uglavnom kao problem rekreativne

matematike. Ovaj problem i njemu sliĉni koji pripadaju oblasti kombinatorike zvanoj blok šeme ili blok

dizajn, imaju direktnu interpretaciju u blok dizajnu. One su blisko povezane sa razliĉitim nauĉnim
disciplinama kao što su:

statistika - kada je reĉ o organizaciji eksperimenata, elektrotehnika-pri konstrukciji kodova koji ispravljaju
greške, projektivna geometrija, itd.

Za rešavanje ovog i niza drugih zanimljivih, praktiĉnih problema postoje odreĊeni prirodni zahtevi o

pravilnom rasporedu u konaĉnim skupovima. Rešenje Kirkmanovog problema vodi do takozvanog
Štajnerovog sistema trojki, nazvanih tako prema radovima Jakoba Štajnera.

U ovom radu ćemo se baviti pronalaţenjem zanimljivih rešenja za Kirkmanov problem i njegovom vezom sa
blok šemama i Štajnerovim sistemom trojki.

Kljuĉne reĉi : skup, taĉka, podskup, blok šeme, Štajnerov sistem trojki.

SUMMARY

th
Kirkman’s schoolgirl problem was intensively studied in the 19 century, mainly as a problem of
recreational mathematics. This problem and similar, which belong to the field of combinatory called block

shemes or block design, have the direct interpretation in the block schemes. They are closely associated with
a variety of scientific disciplines, such as:

statistics – regarding the organization of the experiments, electrical engineering – the construction of the

error – correcting codes, the projective geometry, etc.
For solving this and many other interesting, practical problem, there are certain natural requirements on a

regular schedule in final sets. The solution of Kirkman’s schoolgirl problem leads to the so – called Steiner

triple system, by the works of Jacob Steiner.
In this study, we will deal with finding the interesting solutions for the Kirkman’s problem and its

connection with the block schemes and Steiner triple system.

Key words: set, point, subset, block schemes, Steiner triples system.