DK-GEORGMOHR 1996 Problem 5

In a ballroom, seven gentlemen $A, B, C, D, E, F$ and $G$ sit directly across from seven queens $a, b, c, d, e, f$ and $g$ in random order. When the gentlemen rise and walks across the dance floor to bow to each of their ladies, someone notices that at least two of the men travel equally long distances. Will it always be like this? The figure shows an example. In the example, $|Bb| =|Ee|$ and $|Dd|=|Cc|$ .