3. Werner wants to write a number at each vertex and on each edge of the rhombus shown. He wants the sum of the numbers at the two vertices at the ends of each edge to be equal to the number written on that edge. What number should he write on the edge marked with the question mark?
A 11
B 12
C 13
D 14
E 15
SOLUTION
B

The number on each edge is equal to the sum of the two numbers at the vertices at the ends of the edge. Therefore, the sum of the numbers on two opposite edges will equal the sum of the numbers at all four vertices. Therefore $8+13=9+$ ? and hence $?=12$.