



 
Shankar, For the sum of fourteen + and  1s to equal zero, seven will have to be +, and seven . Note that situation requires an ODD number of each! Now start with all vertices assigned +1; then all faces will also be assigned 1 for a total of 14. Change the sign of a vertex one at a time and note that the vertex and its three adjacent vertices CHANGE sign. After a while a vertex might be surrounded by 0, 1, 2, or 3 negative faces. Check in each case how the number of negative 1s goes up or down. For example, if the vertex goes from + to , and at that time just one of the adjacent faces is , then three items will go from + to  and one goes from  to +. In all we will end up with two more 's and two fewer +'s  in other words, the numbers change by EVEN increments. You should be able to see how the argument goes from here. Chris  


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