How does the Zimmermann Telegram relate to the 2016 theme of the NHD of exploration, encounter and exchange in history?

The Zimmermann Telegram relates most clearly to the theme of encounter, but it can be linked to some degree to exploration and exchange as well.

The clear connection is between this telegram and encounter.  One aspect of encounter can be conflict.  The Zimmermann Telegram came about because of two different conflicts.  First, it came about because of conflicts between Germany and the US-British alliance.  Second, it came about because of conflict between the United States...

The Zimmermann Telegram relates most clearly to the theme of encounter, but it can be linked to some degree to exploration and exchange as well.

The clear connection is between this telegram and encounter.  One aspect of encounter can be conflict.  The Zimmermann Telegram came about because of two different conflicts.  First, it came about because of conflicts between Germany and the US-British alliance.  Second, it came about because of conflict between the United States and Mexico.  If the US had not taken what is now the American Southwest from Mexico in the 1840s, the Zimmermann Telegram would not have been sent. If the British and the US had not been in conflict with Germany in 1917, (I know the US was not at war with Germany yet, but there were clear conflicts between the two), the telegram would not have been sent.  So, the main connection here is that the telegram came about because of encounters/conflicts.

It is also possible to tie the Zimmermann Telegram to exploration and exchange.  Without exploration (and the exchange of germs that went with it), neither the United States nor Mexico would exist in their current forms.  Without exploration, the European countries would not have had empires to fight over and WWI might not have happened.  Thus, exploration and exchange made the telegram possible.  We could also say that the exchange of people and goods helped make the US and the British allies.  Because of exchange, many Americans are of English descent.  Because of exchange, there were economic ties between the US and Great Britain.  These ties helped cause an alliance between the two countries and helped cause Germany to come into conflict with the US.

Thus, all three of the themes of National History Day are present with the Zimmermann Telegram, but the theme of encounter has the strongest connection.