- #1
Hells_Kitchen
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Hi there,
i was wondering if you had any thoughts on the following question:
Let (a_{1}, a_{2}, ..., a_{2n}) be a permutation of {1, 2, ..., 2n} so that |a_{i} - a_{i+1}| \neq |a_{j} - a_{j+1}|, whenever i \neq j.
Show that a_{1} = a_{2n} + n, if 1 \leq a_{2i} \leq n for i = 1,2, ..., n
i was wondering if you had any thoughts on the following question:
Let (a_{1}, a_{2}, ..., a_{2n}) be a permutation of {1, 2, ..., 2n} so that |a_{i} - a_{i+1}| \neq |a_{j} - a_{j+1}|, whenever i \neq j.
Show that a_{1} = a_{2n} + n, if 1 \leq a_{2i} \leq n for i = 1,2, ..., n
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