a solo player competed against a pair of contestants, and hence setting out to prove or disprove the old adage that two heads really were better than one.
According to this article:
Three players competed on each show. Two of the players were related (a "family pair"), and formed a team to play against a solo player. The reasoning for this was "to see if two heads are better than one," as Bill Cullen mentioned often at the top of the show.
WRT the gameplay, this blogpost points out that:
Blockbusters had its roots in a much older board game called Hex, independently invented by John Nash of A Beautiful Mind fame in 1947 at Princeton University
Hex is played by two players, represented by two colors, on an 11-by-11 array of hexagons. The goal of each player is to connect two opposite sides of the board with stones of his or her own color before their opponent does.
One of the problems with Hex, however, lied in its even-sided grid. When all of the grid’s sides are of equal length, the first player has a distinct mathematical advantage. Therefore, the pie rule is put into effect, wherein the second player, after seeing the first player’s move, can elect to change sides with his or her opponent for that game and accept player one’s move as his or her own.
When adapting it for TV, this unfair game-play would be an issue. Also, the number of questions would be too much. Thus the board had to be reduced.
Mr. Ryan solved this problem in two ways. First, he resized the board (now consisting of hexagons filled in with letters of the alphabet) so that the game was played with five columns of four hexagons each. Now, since a board with uneven sides theoretically gave the second player the aforementioned advantage the first player would have had, he added an interesting handicap to the game: a two-player team would play against one solo player. The duo would be tasked with completing the longer connecting path, since there were two brains on that side and only one on the opposing side. Blockbusters was born.