About the task “Knights of the King Arthur” for developing multilevel tasks

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.