The first clue directly reveals Bradley’s activity.
From there, it is known that students with names that are palindromes take part in Gymnastics – there are two such names, Ava and Hannah.
By Hannah’s clue, Mary Jane also takes part in Gymnastics. Since no Gymnastics students can be adjacent (Ava’s clue), and every column has to contain Gymnastics (Lois’s clue), the only position where it can be slotted in the second column is James’s cell.
Also, since Mary Jane’s clue reveals that all activities have to be present in each row, and the bottom row still has no Gymnastics, Susan is taking part in Gymnastics.
From Susan’s clue, Steven and Freddy are taking part in Basketball and Exercise, but it is not yet clear who plays what. However, it leads to the conclusion that Jimmy can only take part in Soccer.
Additionally, by Mary Jane’s clue, Daniel and Michael take part in either Soccer or Basketball, but Soccer is already present in Daniel’s row, so he plays Basketball.
Daniel’s clue reveals that one row’s activities’ starting letters make up a word, and the only English word that can be formed by those letters is the word ‘BEGS’. The only row that could hold this word is the fourth row, which can now be entered. Emily is therefore taking part in Basketball, Michelle in Exercise, and Ellen in Soccer.
Florence’s activity can also be filled, since Exercise is the only activity missing in that row.
Next, Steven’s activity is now clear. It’s Exercise. Therefore, Freddy’s activity is Basketball.
Ellen’s clue reveals that each column has a different doubling activity, and Jimmy’s clue says that only Soccer can be and has to be vertically adjacent to another Soccer. This means that Robert’s activity cannot be Basketball (vertical adjacency to Freddy), nor Exercise (vertical adjacency to Michelle). Since no Gymnastics can be adjacent even diagonally, Robert’s activity is Soccer.
Further, this means that Thomas’s activity is not Soccer, so Soccer has to be doubled in the fourth column.
Finally, the second column needs a repeated activity, and it cannot be Gymnastics (already doubled in the first column) and Soccer (has to go to the fourth). Matilda is vertically adjacent to Michelle who takes part in Exercise, meaning that she can only do Basketball.
The only remaining activity for the bottom row is Michael’s Soccer (since all others have been used). Hank’s activity is then Basketball, and Thomas’s must be Exercise.