Using your Head is Permitted

February 2010 riddle

UPDATE (1 March): No solutions have been submitted so far to this riddle, despite the hint given. The riddle will therefore run one extra month, but this time with a much bigger hint. Click here for the hint.

This month's riddle continues the January one, which is why it must begin with a warning:

Spoiler alert: The following description contains hints regarding the solution of last month's riddle. If you still mean to tackle that other riddle, you may want to hold on before you continue to this one.

The solution to last month's riddle established that Laura the Librarian employs a strategy that will, eventually, cause all n encyclopedia volumes to be properly sorted.

We continue this month by asking how much time (or, equivalently, how many steps) it will take Laura to achieve this goal. Recall that Laura can choose both the initial sorting position and the sequence of sorting steps that she uses, and that her goal is for the sorting to be completed in the largest possible number of steps.

Your answer should include an exact number of steps (expressed as a function of n), an initial arrangement and sequence of steps that would afford this number of steps, and proof that no other arrangement coupled with no other sequence of steps can cause the sorting to last any longer.

Hint: Readers are encouraged to utilize last month's solution.

List of solvers:

Daniel Bitin (7 March 23:37)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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