This is a tough nut but not hard to crack so how about having a go and sending in your solution. This should help you to get started.
<p/>
There are 6 vertices and 5 edges. Let's suppose
the magic constant is <i>h</i> and this is the same at
each vertex.  The total of all the numbers 1 + 2
+ ... + 11 = 66 but the numbers on the edges,
<i>a</i>,<i>b</i>,<i>c</i>,<i>d</i>,<i>e</i> are counted twice. So



<br clear="all" /><table border="0" width="100%"><tr><td>
<table align="center"><tr><td nowrap="nowrap" align="center">
(<i>a</i>+<i>b</i>+<i>c</i>+<i>d</i>+<i>e</i>)+66=6<i>h</i>.</td></tr></table>
</td></tr></table>


<p/>
So <i>a</i>+<i>b</i>+<i>c</i>+<i>d</i>+<i>e</i> is a multiple of 6 and it is at
least 1+2+3+4+5=15 so it must be 18 or more.
Hence 6<i>h</i> &#8805; 84 and <i>h</i> &#8805; 14.
<p/>
Now you need to consider several cases for different values of <i>h</i>, starting with <i>h</i>=14, and for each value of <i>h</i> you have information about the sum of the numbers on the five edges. Also for the feet you have to find 4 pairs of numbers adding up to <i>h</i>.