Maths Olympiad Prep

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Combinatorics Difficulty 4.9 AIME Find the answer

5. In the store "Third is Not Excessive," there is a promotion: if a customer presents three items at the cash register, the cheapest of them is free. Ivan wants to buy 11 items costing 100,200,300,,1100100, 200, 300, \ldots, 1100 rubles. For what minimum amount of money can he buy these items?

A number or a short expression. Spacing and $ signs are ignored.

Solution

Answer: 4800. It is clear that items should be listed in descending order of price, then the cost of the purchase will be 1100+1000+800+700+500+400+200+100=48001100+1000+800+700+500+400+200+100=4800 rubles.

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