One-way roads: Difference between revisions
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==Puzzle== | ==Puzzle== | ||
A county has n > 4 cities. Is it possible to connect some pairs of cities by one-way roads so that one can travel from every city to every other city using only one or two roads? If so, how? Note that for every pair of cities A and B, only one road connecting A with B is allowed; this road leads from A to B or from B to A, but not both ways. | A county has <m>n > 4</m> cities. Is it possible to connect some pairs of cities by one-way roads so that one can travel from every city to every other city using only one or two roads? If so, how? Note that for every pair of cities A and B, only one road connecting A with B is allowed; this road leads from A to B or from B to A, but not both ways. | ||
[[Category: Graph theory]] | [[Category: Graph theory]] | ||
[[Category: New]] | [[Category: New]] | ||
[[Category: Needs solution]] | [[Category: Needs solution]] | ||
Current revision as of 19:11, 24 July 2017
Found this one on the SUNY Stony Brook Math Problem of the Month archives.
Puzzle
A county has <m>n > 4</m> cities. Is it possible to connect some pairs of cities by one-way roads so that one can travel from every city to every other city using only one or two roads? If so, how? Note that for every pair of cities A and B, only one road connecting A with B is allowed; this road leads from A to B or from B to A, but not both ways.