you are given a set of tiles which are numbered from 1 to 121 you do the following operations repeatedly you remove all those tiles that are numbered with a perfect square and the renumber the remaining tiles consecutively starting with 1 how many times must you perform the operation before you are left with 1 tile
Answers
Answer:
20
Step by Step Explanation:
Let us see the number of tiles with perfect square number on them: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121.
11 tiles will be removed, and we're now left with 121 - 11 tiles, or 110 tiles. Now the tiles with perfect square number on them will be: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
10 tiles are removed again, now we're left with 110 - 10 = 100.
Similarly this time the maximum number is 100, so there will be 10 tiles with perfect square on them.
After 10, there'll will be 100 - 10 = 88, so there will be 9 numbers with perfect squares.
We can see that we removed 10 tiles two times, and then 9 tiles two times, and in a similar manner we'll have to remove them two times till the number reaches 1.
This means the number of times this operation has been re done will be 2 x 10 = 20.
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