Pathways Investigations Some ideas

Here are some discoveries you may have found out about pathways

You will have discovered that there is something special about networks that can be traversed (made into complete pathways).

Where two matches meet they must look like this

Where 4 matches meet the must look like this

Networks with just even junctions are easily traversable

Networks with any number of even junctions and two odd junctions are traversable

Networks with more than two odd junctions are not traversable

Where there are odd junctions they must either be the beginning or the end of the pathway

To make a traversable pathway with matches:

· At even junctions there should be the same number of “heads” and “tails”.

· Where an odd number of matches meet then there must be just one more “head” or one more “tail”.

Number of solutions

If we fix the starting point there are 6 possible pathways around the network. Given that there are 2 starting points that makes 12 solutions in all. When we show these with matches each solution gives represents two possible options so if we take one starting point there are only three match solutions.

With both of the slightly more complex networks ( Two 3-junctions and a 4-junction) there are 16 possible pathways. Both of the networks given are in fact equivalent to each other..topologically equivalent)

More Pathway Puzzles