Clever Cigar Seller
Mr. Cigarman sells fresh cigars at each and re-rolled cigars at each.
He buys his fresh cigars at for a pack of 100 cigars. He makes re-rolled cigars himself. Each re-rolled cigar needs 4 used cigars costing each and incurs a labour cost of to make. Cigar butts can be re-rolled any number times.
Eg : If one starts with 20 cigars, the resultant 20 butts can be used to make 5 cigars. 4 of these 5 butts can be re-rolled again to get one more cigar.
If Mr. Cigarman buys 10 packs of cigars, and is only allowed to buy back the cigar butts that he sold to his customers, what is maximum amount of profit that he can earn from that stock.
The answer is 2333.
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1 solution
Each fresh cigar is sold at a profit of $ 2 and each re-rolled cigar is sold at a profit of $ 1 .
The stock of 1000 fresh cigars will fetch a profit of $ 2 0 0 0 .
From the 1000 butts we get 250 cigars. (1st generation)
From the 250 butts we get 62 cigars + 2 butts extra (2nd generation)
From the 62 butts + 2 butts from last generation, we get 16 cigars (3rd generation)
From the 16 butts we get 4 cigars (4th generation)
From the 4 butts, we get 1 more cigar.
Thus, Mr. Cigarman can make 2 5 0 + 6 2 + 1 6 + 4 + 1 = 3 3 3 re-rolled cigars earning a further profit of $ 3 3 3 .
Thus, the total profit is 2 0 0 0 + 3 3 3 = 2 3 3 3 .