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2018 BIMC keystage3-IWYMIC team Question 10

xIMC · 2018 BIMC keystage3-IWYMIC team

Question 10

Tom writes down the number 1. For any number $n$ already written down, Tom writes down the numbers $5n$ and $5n+1$, provided that they are less than 1000. Jerry computes all sums of two different numbers Tom has written down. How many different sums does Jerry get?

Show your full solution.

Answer: ______