a set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all riles 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?
2007-12-01 12:07:08 · 3 answers · asked by ~USA~ 2 in Education & Reference ➔ Homework Help
18 operations.
2007-12-01 12:18:27 · answer #1 · answered by Anonymous · 0⤊ 1⤋
There are 10 perfect squares from 1 to 100.
(1, 4, 9, 16, 25, 36, 49, 64, 81, 100).
Remove them and you have 90 left.
There are 9 perfect squares from 1 to 90.
There are 9 perfect squares from 1 to 81.
There are 8 perfect squares from 1 to 72.
There are 8 perfect squares from 1 to 64.
There are 7 perfect squares from 1 to 56.
There are 7 perfect squares from 1 to 49.
There are 6 perfect squares from 1 to 42.
There are 6 perfect squares from 1 to 36.
There are 5 perfect squares from 1 to 30.
There are 5 perfect squares from 1 to 25.
There are 4 perfect squares from 1 to 20.
There are 4 perfect squares from 1 to 16.
There are 3 perfect squares from 1 to 12.
There are 3 perfect squares from 1 to 9.
There are 2 perfect squares from 1 to 6.
There are 2 perfect squares from 1 to 4.
There is 1 perfect square from 1 to 2.
Remove it and you are left with 1.
Note that you remove 9 twice, 8 twice, etc.
The only numbers you remove once are 1 and 10.
The operation has to be performed 18 times.
2007-12-01 20:25:04 · answer #2 · answered by Steve A 7 · 1⤊ 0⤋
There are 10 perfect squares from 1-100.
Subtract that from 100= 90.
There are 9 perfect squares from1-90.
Subtract that.
Do that so on and so forth... and you'll get your answer. :)
2007-12-01 20:15:14 · answer #3 · answered by Sara Mascara★. 5 · 2⤊ 0⤋