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21

Here's an optimal procedure that lets you find out the status of every person after exactly questions: Reasoning: Proof of optimality:

6

Firstly, the bottles: Now let's compare prices of the two different types of alcohol purchases: In total you need 32 times 500 ml, which is 66⅔ times 240 ml or 200 times 80 ml. Firstly, buy After all that, you still have one coupon in hand and 1600 ml left to get (that's 6⅔ times 240 ml or 20 times 80 ml). Now buy So the overall expenditure is

4

A better upper bound is Solution: P.S.

3

You can solve the problem via integer linear programming as follows. There are only nine useful purchases to consider, and I enumerated them by hand: 2 80mL bottles: cost \$20 1 240mL bottle: cost \$36 1 PET bottle: cost \$5 3 240mL bottles, 1 coupon: cost \$52 1 240mL bottle, 2 80mL bottles, 1 coupon: cost \\$41 1 240mL bottle, 9 PET bottles, 1 coupon: ...

3

A naive upper bound is EDIT:

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