14 December 2005

Puzzling Wednesday

A legendary city was said to have been built on seven islands that were connected to each other and the mainland as follows: Each island had the same number of connections as its rank in size. So, the largest island had 7 connections, the second largest 6, and so on until the smallest island, which had only 1 connection. And the mainland had but one connection to one of the islands.

If the legend is taken literally, explain why no such city could have existed.

This should be easy. I will post the answer in comments tomorrow.

Modified from puzzle #83 in C.R. Wylie, Jr., 101 Puzzles in Thought & Logic, Dover Publications, 1957.


Roger B. said...

I suspect it's mathematically impossible, but it would also be completely impractical because the connections would criss-cross each other many times!


The total number of connections, being twice the number of bridges, must be an even number. For example, if there is 1 bridge between 2 islands, each has 1 connection adding up to a total of 2 connections. The total number of connections in the legendary city add up to 29 (7+6+5+4+3+2+1+1). Therefore, the legend is not accurate.