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Question

A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one?

Accepted Answer

The pattern is quite simple to see after listing a couple of terms. array|r|r|r| #&Removed&Left 1&10&90 2&9&81 3&9&72 4&8&64 5&8&56 6&7&49 7&7&42 8&6&36 9&6&30 10&5&25 11&5&20 12&4&16 13&4&12 14&3&9 15&3&6 16&2&4 17&2&2 18&1&1 array Thus, the answer is 18.