perplexus.info :: Numbers : Any order will do

Any order will do (Posted on 2005-07-12)

The numbers from 1 to 2n are separated into two lists of n numbers each, A and B; elements are ordered so a₁<a₂<...<a_n and b₁>b₂>...>b_n.

How much is |a₁-b₁|+|a₂-b₂|+...+|a_n-b_n|?

See The Solution Submitted by Federico Kereki

Rating: 3.6667 (3 votes)

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re: thoughts

| Comment 2 of 8 |

(In reply to thoughts by Josh70679)

If I take |1-4|+|2-3|, the first pair differs by 3>2=n, but the second pair only differs by 1 which compensates. However, individual terms can exceed n.

Posted by Richard on 2005-07-12 17:15:22

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