SOLUTION: A set of tiles numbered 1 through 100 is modified repeatedly by the folowing operation: remove all tiles numbered with a perfect square, & renumber the remaining tiles consecutivel

Question 39128: A set of tiles numbered 1 through 100 is modified repeatedly by the folowing operation: remove all tiles numbered with a perfect square, & renumber the remaining tiles consecutively strarting with 1. Howmany times must the operation be performed to reduce thenumber of tiles in the set to one?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
There is no method for this except just doing the procedure...
The perfect squares are
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100
Thus the first time ten tiles are removed and 90 remain.
The second time nine tiles are removed and 81 remain.
The third time nine tiles are removed and 72 remain.
The next time eight tiles are removed and 64 remain.
The next time eight tiles are removed and 56 remain.
The next time seven tiles are removed and 49 remain.
The next time seven tiles are removed and 42 remain.
The next time six tiles are removed and 36 remain.
The next time six tiles are removed and 30 remain.
The next time five tiles are removed and 25 remain.
The next time five tiles are removed and 20 remain.
The next time four tiles are removed and 16 remain.
The next time four tiles are removed and 12 remain.
The next time three tiles are removed and 9 remain.
The next time three tiles are removed and 6 remain.
The next time two tiles are removed and 4 remain.
The next time two tiles are removed and 2 remain.
The last time we remove one tile and one remains.
Now count up the times...18 times?
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