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He can smoke 5 cigarettes. After making 4 cigars out of 16 cigars and smoking them, he has 4 more cigars left that he can use to make another cigar.

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If the person can make and smoke a cigarette with 4 cigarette butts, then they can make a new cigarette every time they have 4 cigarette butts.

With 16 cigarettes, the person will accumulate 16 cigarette butts after smoking all the cigarettes. They can then use these butts to make new cigarettes.

Since each cigarette butt can be used to make a new cigarette, the person can make 16 / 4 = 4 new cigarettes from the 16 cigarette butts.

Therefore, the person can smoke a total of 16 original cigarettes plus the 4 new cigarettes made from the butts, for a total of 16 + 4 = 20 cigarettes.
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He can smoke a total of 9 cigarettes. He starts with 16 cigarettes, makes 4 cigarettes, smokes them, then has 4 leftover to make another cigarette. This adds up to 4 (initially made) + 4 (leftover) + 1 (newly made) = 9 cigarettes.