Solution
Alon, Caro, Krasikov and Roditty showed that 1 + log2(n) is sufficient, using a cleverly enhanced inclusion-exclusion principle.
Radcliffe and Scott showed that if n is prime, 3 is sufficient, and for any n, 9 times the number of prime factors of n is sufficient.
Pebody showed that for any n, 6 is sufficient.
Read more about this topic: Necklace Problem
Famous quotes containing the word solution:
“I herewith commission you to carry out all preparations with regard to ... a total solution of the Jewish question in those territories of Europe which are under German influence.... I furthermore charge you to submit to me as soon as possible a draft showing the ... measures already taken for the execution of the intended final solution of the Jewish question.”
—Hermann Goering (1893–1946)
“All the followers of science are fully persuaded that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they can be applied.... This great law is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate is what we mean by the truth, and the object represented in this opinion is the real.”
—Charles Sanders Peirce (1839–1914)
“Any solution to a problem changes the problem.”
—R.W. (Richard William)