Following the method (and language) of the solution to the first problem it is now clear that, indeed, the above design cannot be properly traced: there are six intersections (not zero or two) with an odd number of streets emanating from them. We suspect, however, if the diagram possessed just two "odd intersections," then we might be able trace the figure. One approach to our challenge problem is to simply change the question! Let’s add streets to the figure to create a map with only two odd intersections. Given that there are currently six troublesome intersections, the addition of two streets would do the trick (and no less). Here’s one possibility with the two remaining odd intersections are highlighted.

By trial and error, we can see that this new diagram can be traced. (The numbers indicated the order of streets to follow.)

This is all well and good, but the streets numbered "3" and "20" are, after all, artificial. Removing these duplicate streets from the diagram to return to the original design is possible, but it means streets “4” and “21” will each need to be traversed twice to compensate for their removal. This shows that two streets must be reused (and no less) to trace the design of the challenge problem with a pencil.

For more on this, click here.