Draw It First

The importance of drawing diagrams cannot be overstated. Consider that although humans have been using written language and mathematics for only a few thousand years, they have been evolving to analyze visual problems (for example, can that rhinoceros catch me before I get to that tree?) for millions of years. Humans are generally much better suited to solving problems presented in pictures than those presented in text or numbers. As the saying goes, “a picture is worth a thousand words.” This maxim also applies to technical interviews.

In some cases, the “actors” in these brainteasers are static, but more often they change or move. When this is the case, don’t draw just one picture, draw many pictures. Make a diagram for each moment in time for which you have information. You can often gain insight by observing how the situation changes between each of your diagrams.

Most graphical problems are two-dimensional. Even when a problem involves three-dimensional objects, the objects are often constrained to the same plane, enabling you to simplify the problem to two dimensions. It’s much easier to diagram two dimensions than three, so don’t work in three dimensions unless you must.

If the problem is fundamentally a three-dimensional problem, assess your relative abilities with drawing and visualization before proceeding. If you’re not good at drawing, your diagram of a three-dimensional problem may do more to confuse than elucidate. On the other hand, if you’re a good artist or drafter, but have trouble with visualization, you may be better off with a diagram. Whatever approach you take, try to attack spatial problems spatially, not with computation or symbolic mathematics.