The Challenge of Creating a GRACEFUL NETWORK 
Here is a puzzle using networks that just might become addicting: Start with a network that has n arcs. (The networks on the background of this page have four nodes and 6 arcs.)Name each node with a different number from 0 to n. Then number each arc by the absolute value of the difference of the nodes it connects.For example, look at the "graceful" network here.The arc connecting nodes 5 and 2 is named 3 because 5  2 = 3.The goal is to name the nodes in such a way that the n arcs are numbered with all the integers from 1 to n.If you can do it,...you will have created a Graceful Network .

We at the math lab know that the networks below can indeed be made "graceful". Give them a shot. We ranked them in order of difficulty. It will probably take you several tries before you get them all. .................................... .........A....................B...........................C HAVE FUN..when you get one it is a real rush! 
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