This Activity is meant for Boy Scouts.

pre-made questions and answers, segregated by difficulty for each rank - tenderfoot, 2nd class, 1st class. Have lots of questions - see this List of Scout Questions

Arrange an imaginary baseball diamond by placing paper squares or cardboard on the floor.

If you have more than 2 patrols, make a baseball diamond for each pair of patrols so you can have multiple games going on at once. Use your oldest patrol as the umpires if needed or if there is an odd number of patrols.

The Pitcher is a leader that asks the questions. He can also be umpire and scorekeeper, but additional helpers for those tasks are good to have.

One patrol is in the field - put a member on each base, catcher, and then outfielders.
The other patrol is up to bat. One scout comes to the plate.
The Pitcher asks the scout a question appropriate to his rank. If the scout answers correctly, he gets a hit and advances to first base. If he wants to go for a 'double' he can have the Pitcher ask a question of the first baseman. If the first baseman answers correctly, the runner is out, otherwise he advances to second base. At second, he can request that the second baseman try to answer the same question or he can just stay. This can be repeated at third and homeplate for a homerun.
If a runner is on first and a batter gets a hit, the batter and runner both advance one base. The batter decides if extra bases should be attempted but the question is put to the baseman where the lead runner is standing. (This gives 2nd, 3rd, and home more chances to answer).
Whenever a runner is coming home and the catcher needs to answer a question, he can get advice from the outfielders.

If the batter answers the initial question incorrectly, it is a pop-up. All the players in the field can discuss the question and the catcher then gives the answer. If correct, the batter is out, otherwise, it is one strike.