30. At the Duchess's, the Cook's, and the Cheshire Cat's

- I want to offer you a most intriguing task,- said the Gryphon. - One day, the Mock Turtle, the March Hare, and the Dormouse decided to visit the Duchess, the Cook, and the Cheshire Cat. Upon arriving, they found that no one was home. On the kitchen table, they saw a plate with pretzels. The Mock Turtle first ate half of the pretzels and then, thinking about it, ate one more pretzel. The March Hare ate half of the remaining pretzels and one more pretzel. Then the Dormouse ate half of the remaining pretzels and one more pretzel. At this point, the Cheshire Cat returned and ate half of the remaining pretzels and one more pretzel, after which there were no pretzels left on the plate.

How many pretzels were there at first?
30. At the Duchess's, the Cook's, and the Cheshire Cat's. The Cheshire Cat must find 2 pretzels on the tray: after eating half of the pretzels and one more pretzel, nothing will be left on the tray. Sonya must find 6 pretzels on the tray: after eating half of the pretzels and one more pretzel, 2 pretzels will be left for the Cheshire Cat. The March Hare saw 14 pretzels on the tray: after eating 7 pretzels and one more pretzel, 6 pretzels were left. The Mad Hatter saw 30 pretzels: after eating 15 pretzels and one more pretzel, 14 pretzels were left.

Thus, there were 30 pretzels on the tray at first.