The closed line segment I is covered by finitely many closed line segments.
Show that one can choose a subfamily S of the family of line segments having the properties:
(1) the chosen line segments are disjoint,
(2) the sum of the lengths of the line segments of S is more than half of the length of I.Show that the claim does not hold any more if the line segment I is replaced by a circle and other occurences of the compound word ''line segment" by the word ''circular arc". combinatorics unsolvedcombinatorics