# Which Way did the bicycle go?

I found this puzzle which simply asks which way was the bicycle going, from its wheel marks on the mud shown in the image

Now there is a simple way to find which mark(line) was made by the front and which was made by the rear wheel because

We know that the tangent drawn anywhere on the line drawn by the rear wheel will always cut the line made by the front wheel . And this is not guaranteed for the front wheel.

How can i use this information to solve it ?

If you look at the left (or the right)of your picture, the upper line shows the fore wheel. I could determine that because the fore wheel of a bicycle oscillates more than the rear one. To determine the direction, choose some points in the rear wheel's trajectory and draw the tangents in those points. The distance between the forward and the back wheel is constant, so you just have to find out which of the segments determined by the tangent and the intersection with the other curve have the same length. If my paint drawing is correct, the left segment is always constant, so the bike is coming from RIGHT (the direction of a bike is the vector from the aft wheel to the forward wheel.

• This argument could be improved by showing a tangent of the front track that doesn't cross the rear. – ColBeseder Mar 21 '15 at 19:07
• Thanks for the tip! I've edited the picture and and added the purple tangent, which doesn't intersect the other curve. – leoll2 Mar 21 '15 at 19:28
• I agree with your answer although there is also the small possibility that a very skilled rider could be riding a 'fixie' backwards. – Penguino Mar 22 '15 at 1:28