during the months of August and September)
The announcement states that
This competition is to take the place of our
system of purchasing problems and games. It will be continued throughout the
year—prices of a similar character being offered quarterly.
Separate prizes was also awarded for the best game and the most brilliant game contributed during Aug.-Oct., 1877.
The earliest known reprint of both problems together is currently the one cited above. Earlier reprints of single problems are known (see YACPDB), and have been examined for traces of the missing problems
Find and consult Danbury News for additional information. (Not sure what the source of the #2 motto is ...)
Prize: Best #2: C. A. Gilberg
Key: 1. Qf1
Source: Scientific American Supplement 5/112 (1878-02-23), p. 1788, prb. 57
Prize: Best #3: C. A. Gilberg
Key: 1. Na6
Source: Scientific American Supplement 5/112 (1878-02-23), p. 1788, prb. 56