7. The diagram gives the lengths of six lines meeting at a point. Eric wishes to redraw this diagram without lifting his pencil from the paper. He can choose to start his drawing anywhere. What is the shortest distance he can draw to reproduce the figure?
A $14 \mathrm{~cm}$
B $15 \mathrm{~cm}$
C $16 \mathrm{~cm}$
D $17 \mathrm{~cm}$
E $18 \mathrm{~cm}$
Solution
B

The shortest total distance is found by starting and finishing on the longest lines. Every other line must be navigated twice, out from the centre and then back.

So the minimum length, in $\mathrm{cm}$, will be found by $3+2+2 \times(2+1+1+1)$, which is $15 \mathrm{~cm}$.