Provided n^3 unit cubes, n > 1 which are numbered from 1 to n^3. All these unit cubes are put together to form a cube with side length n. In this cube two unit cubes will be neighbors if they share at least one vertex. As distance of two neighbor unit cubes we define the absolute value of the difference of the numbers assigned to those two unit cubes. Imagine for all possible compositions of the "big" cube the biggest distance among any of these two unit cubes - all these maximal distances are written on a board. What is the minimal number on the board ?
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1 Answers
1this was a good problem which i thought some one would take interest in.
ok please see this:
http://www.mathlinks.ro/viewtopic.php?t=5709
the reply by grobber over there is just so beautiful..