Most team-building activities reward the people who are already comfortable speaking up. A mystery case does the opposite. The evidence is written down, so the person who reads carefully has as much standing as the person who talks fastest — and the breakthrough usually comes from someone noticing a detail rather than someone taking charge.
It also produces a real decision under uncertainty. The group has to commit to an answer knowing it might be wrong, which surfaces how a team actually handles disagreement far more honestly than an exercise about handling disagreement.
For a session of eight or more, run parallel groups of four to six on the same case and compare conclusions afterwards. Two teams reaching different verdicts from identical evidence tends to be the most useful twenty minutes of the day.