# Knighted!

A graph with 64 nodes represents the squares of a chessboard. The nodes are joined appropriately by edges, each representing a move of the knight. In this graph, every node will be of degree two, three, four, six, or eight. Let the values $$a,b,c,d$$ and $$e$$ be the number of nodes with each respective degree such that $$a$$ is the number of nodes with degree two, $$b$$ is the number of nodes with degree three, etc. What is the value of $$a+c+e?$$

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