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Mathematical problems (with the help of mathematical experts)
The answer is: five at most.

Group discussion:

Each question has four options, and each question counts as one round, so each round needs to divide 16 people into four groups, and one group corresponds to 1 option. We need to ensure that those who already belong to the same group can no longer belong to the same group.

First of all, if a group consists of five people, then these five people can't be in the same group in the next round, but there are only four groups, which means that each group can't exceed four people, so the only grouping method is: four people in each group in each round.

Then, for anyone, he can group with three different people in each round. In addition to himself, there are still 15 people left, so these 15 people can be grouped by 15 ÷ 3 = 5 (rounded) and will not be repeated. If it exceeds 5 rounds, it must be repeated.

To sum up, it is divided into 4 groups, with 4 people in each group, and can be divided into 5 rounds at most, without repetition. So five topics at most.