The statement of the problem was ambiguous. I'll repost
this interesting problem, with more exact conditions, next semester. The
intent was that the cards should be contiguous at all times --- no holes between
them. Without this condition, the problem is trivial: move the 7 two steps
to the right, then move the 6 four steps to the right, and so on. With
this added proviso the minimal number of moves, m(n), needed to
reverse n cards is given in the table below.
|
n |
2 |
3 |
4 |
5 |
| m(n) |
2 |
10 |
32 |
68? |
The value of m(5) is an upper bound, which I believe to
be exact. Can you find more terms for m(n)?, maybe an upper
bound? I don't know of a general expression for m(n).
Can you find one?
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