Saturday, 14 December 2013

New Scientist Enigma 152: The highways of Genoland revisited

Following my post on The highways of Genoland, Jim Randell pointed out that the original puzzle had missed a round trip, and that there are actually four round trips. The missing round trip uses highways 1,2,3,4,D (not necessarily in that order).

I wondered what a solution would look like if the fourth round trip had been included in the original puzzle:

As before, no pair of cities is connected by both a national and provincial highway. There are two possible configurations of connections that have eight connectors connecting five nodes:

Configuration A does not provide four round trips, so the five cities are connected in configuration B. We can immediately deduce which city is Geno:

The four  round trips 1,3,4,B,C;   1,2,A,C,D;   2,3,A,B,C;   1,2,3,4,D are in some order: 


Highways 1,2,3,C appear in three round trips (green). 4,A,B,D appear in two round trips (orange)

Geno is reached by the highways that appear in two round trips, namely 4,A,B,D


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