Tim wants to draw the figure shown without lifting his pencil off the paper. The lengths of the lines are given in the figure. He can choose to start his drawing anywhere. What is the shortest distance he could draw to complete the figure? To minimize the total distance we travel, we should minimize the times that we have to cross the longest lines. Therefore, we should start with the 3 cm line, because we only have to traverse it once, and then we can traverse the 1 cm, 1 cm, and 1 cm lines twice, and then one of the 2 cm lines twice, and then a 2 cm line for the final time without traversing that one twice. Therefore, the total distance is 15 cm.

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