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MathNet 2010 — Part 01 Question 48

Math Olympiad Vault · MathNet 2010 — Part 01

Question 48

We consider a group of trees in a nature reserve, all of which have a positive integral age. The average age is 41 years. After destruction of a tree with an age of 2010 years by lightning, the average age of the remaining trees is 40 years.

Determine the original number of trees in the group. What is the maximal number of trees of an age of 2010 years in the original group?