Geodesic
About the task ``Knights of the King Arthur'' for developing multilevel tasks
Matematičeskoe obrazovanie, Tome 93 (2020) no. 1, pp. 24-27

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Solutions to the problem of selecting “non-neighboring” objects are given. The cases of placing objects on a circle and on a straight line are considered. The irreversibility of the arrangement and selection of homogeneous objects in combinatorics is noted. A method of selecting “non-neighbors” is proposed, which is based on the interpretation of the concept of “non-neighbors” as objects separated by a common “neighbor”. Algorithms for selecting even and odd numbers of objects and a method for “through one” selecting are proposed.
Keywords: combinatorial problems, restrictions on the order of choice. 
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     author = {V. K. Gavrilov},
     title = {About the task {``Knights} of the {King} {Arthur''} for developing multilevel tasks},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {24--27},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2020_93_1_a2/}
}
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V. K. Gavrilov. About the task ``Knights of the King Arthur'' for developing multilevel tasks. Matematičeskoe obrazovanie, Tome 93 (2020) no. 1, pp. 24-27. http://geodesic.mathdoc.fr/item/MO_2020_93_1_a2/