A game that can be used for problem solving or just as a fun activity. I was initially worried about running this because there is a level of strategizing to it that the Scouts might have been dubious about on some nights. But actually, after the first game they were startlingly enthusiastic for a second one.
Settlers of Catan is a game that I've tried adapting to various ideas because it comes with a lot of useful options for setting up games. This is probably the most successful to date.
Settlers of Catan basic set (5-6 player expansion for more teams).
If you don't have this then you can produce your own set to fit the rules as follows:
> 5 Resource types (teams will hoard 20 cards at a time sometimes, so provide a decent number; this is one reason that Settlers is useful because it provides a good sized pile)
> Tokens for road (10+ per team)
> Tokens for settlements (5+ per team)
> Tokens for cities (4+ per team)
> Reference card showing costs and points
1 leader as bank
1 leader as property manager
1+ leader managing teams
Divide into teams.
For using Settlers pieces, assign each team a colour and give them the reference card of that colour; otherwise simply give them a reference card each.
Set each team up at one end of a room with a table or other suitable surface to work on.
The bank and property manager set up at the other end of the room with the resources and tokens respectively.
One Scout at a time from each team can run up to the leaders at the far end of the room. To begin with they take one random resource card from the bank and return it to their team. Next Scout runs. Repeat.
Once the resources have been acquired to produce something, these resources are taken to the property manager and traded for the item in question:
> Road (1 wood, 1 brick)
> Settlement (1 wood, 1 brick, 1 wheat, 1 sheep)
> City (2 wheat, 3 rock, a Settlement must be handed over to be upgraded)
> Any 3 resources can be traded for 1 of something else (3 wheat become 1 brick for instance)
Each item purchased is scored as follows:
> Settlement = 1 point each
> City = 2 points each
> Road = 2 point for the team with the most road (other teams must exceed this amount of road to claim the points)
For a roughly 10-15 minute game we played in a hall to 10 points; going for more than 10 points may be tricky when playing with Settlers pieces (4 cities + 5 settlements + longest road can only give 15 points maximum).
Leaders not acting as bank or property manager will need to keep track of the points that each team has in order to determine the winner and ensure that Scouts are not sending more than one person at a time.
For younger sections this can be made easier by having a young leader assisting with strategy. For older sections the Development Cards can be brought into play (highest number of Knights gives 2 extra points, road builder gives two free roads, etc).
A slower version of this might be to make it turn-based rather than real-time; teams get dealt cards in turn rather than being based on how fast they come to collect them. This gives more time for thinking and planning rather than