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IMSO 2006 Mathematics – Taiwan Selection – Exploration Question 4

IMSO Maths · IMSO 2006 Mathematics – Taiwan Selection – Exploration

Question 4

The menu in the school cafeteria never changes. It consists of 10 different dishes. Peter decides to make his school lunch different every day, with at least 1 dish. For each lunch, he may eat any number of dishes, but no two are identical.

(a) What is the maximum number of days Peter can do so?

(b) What is the total number of dishes Peter has consumed during this period?