This is not the exact same by any means, but reminded me of a story my dad told me. Sometime in the 60s a radio station had a contest where you had to guess the top 5 songs of the week in the proper order (1-5) and the winner would get $1000. To make a guess you had to mail in an index card numbered 1-5. Maybe 10 or so songs were likely to be in that top 5, so my dad guessed guessed every permutation. The cost was the price of a stamp for each index card but he did end up winning.
This is hard to believe. 10 permute 5 is just over 30,000. Unless stamps were less than 3 cents, that scam wouldn't work.
First class stamps have been 4 cents since 1958. Not to mention the labor of preparing 30,000 index cards.