OLYMPIADS IN INFORMATICS, 2018, Vol. 12, pp. 111 - 117
© IOI, Vilnius University
ISSN 1822-7732
DOI: 10.15388/ioi.2018.09
Combinatorial Property of Sets of Boxes in Multidimensional Euclidean Spaces and Theorems in Olympiad Tasks
Pavel S. PANKOV1, Azret A. KENZHALIEV2
1International University of Kyrgyzstan
2American University of Central Asia
e-mail: pps5050@mail.ru, azret.kenzhaliev@gmail.com
Abstract
Theorems (in general sense) are constituents of inventing, analysing and solving olympiad tasks. Also, some theorems can be proved with computer assistance only. The main idea is (human) reducing of primary (unbounded) set to a fnite one. Non-trivial immanent properties of mathematical objects are of interest because they can be considered as alternative defnitions of these objects revealing their additional features. A non-formal indication of such property is only inital data (size of domain) and only output data (proven/not proven) in a corresponding algorithm. One new and two known examples of such properties are considered, some techniques to convert theorem-proving algorithms into olympiad tasks are proposed.
Keywords:
olympiads in informatics, immanent property, task, theorem, unboundedness.
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Copyright © International Olympiad in Informatics, 2018
Vilnius University, 2018
