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MathNet 2024-part-06 — 165 problems (EN–VI) Question 28

Math Olympiad Vault · MathNet 2024-part-06 — 165 problems (EN–VI)

Question 28

Sugar Station sells 44 different kinds of candies, packaged one to a box. Each box is priced at a positive integer number of cents, and it costs 1.51 dollars to buy one of every kind. (There is no discount based on the number of candies in a purchase.) Unfortunately, Anna only has 0.75 dollars.

a) Show that Anna can buy at least 22 boxes, each containing a different candy.

b) Show that Anna can do even better, buying at least 25 boxes, each containing a different candy.