There are two methods to select the Team Challenge. The team (kids) selects the challenge with the coaches facilitating the process or the coach picks a challenge. Both have their advantages and disadvantages. The first year I coached, we let the team select the problem. Subsequent years I/coaches selected the problem.
I have been selecting the problem for the team for these reasons:
1) We get organized and have our first meeting in early December which results in about 10 meetings before the first tournament. Selecting the problem can use up several of those scarce meeting slots. I like the team to be prepared and relaxed at the tournament. Giving the team as much time as possible to work on the challenge is one way to help accomplish that. Using up several of the meetings selecting a problem makes the season feel rushed and adds un-needed stress to the team.
2) Unfortunately the process of selecting the challenge leads to a feeling of "winners" and "losers" where the team members that get their problem selected win, and the team members that don't get their selection feel disappointed. Also, most of the team members don't get to work on their first choice. I don't like to start a season on this note.
3) There are plenty of opportunities for the team to work on compromising and problem resolution skills during the season. I like the team to apply their energy to the problem solution, and not to the problem selection.
This is why I like to simply select a problem that looks like there is something interesting for everyone and start to focus on the problem at the first meeting.