Consider the apparatus shown in Figure 3.9. Note that there are 12 chutes (numbered 1 to 12), and a ball dropped into a chute will slide down the tube until it reaches an AND-gate or an OR-gate. If two balls reach an AND-gate, then one ball will pass through, but if only one reaches an AND-gate, it will not pass through. If one or two balls reach an OR-gate, then one ball will pass through. The object is to obtain a reward by having a ball reach the location called REWARD. What is the fewest number of balls that can be released in order to gain the reward?

Figure 3.9

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2 3 OR AND AND 5 6 7 8 9 10 11 12 AND OR AND REWARD AND OR AND AND OR