I would ignore the letter just like I ignore all the Nigerian lottery emails.
Nobody gives that kind of money. You have to be super gullible not superrational to participate in such a game.
Assume you know with certainty the contest is real the money and giveaway are real and the terms of the contest will be honored. Its been in the news and the judges are third parties. Furthermore the letter can be verified to have come from the contest.
Obviously, no one would respond to a Nigerian lottery email that is not the point of this exercise.
Even under these conditions, you have very slim chances of winning.
I would assume more than 5% of people are greedy, even among rational thinkers there will greedy a-holes who would act against their rational thinking, and send the telegraph with their name.
Waste of time either way. You dont enter, you lose. You enter, you almost certainly lose as there will more than one person who sent the telegraph.
Like I said, a waste of my time.
Even in the most communist societies you will find that more than 5% of the population is greedy and would take free stuff without hesitation.
If you send these letters to the very top one percenters, you might change the odds, but with the general population there is no way to win this game, so why bother playing.