The set {2,3,5, 6, 7, 8, 10, 11, …..} consists of all the positive integers that are not squares.?
The set {2,3,5, 6, 7, 8, 10, 11, …..} consists of all the positive integers that are not squares.When listed from least to greatest, what is the 2010th element in this set?
2010 – number of squares from 1 to 2010
Calculate largest square number before 2010:
sqrt(2010) = 44.83
44^2 is the largest square.
So there are 44 squares before 2010.
The series grows by +n where n is the missing numbers, so:
We need to add that on, so 2010 + 44 = 2054
Our first estimate is 2054.
Largest square before 2054:
sqrt(2054) = 45.32
i.e. 45
If this was still 44 rather than 45 then the answer would be 2054, however we now have one more number missing, so the sequence has grown by +1.
so 2054 + 1
Answer = 2055
a third Hollywood Squares 1968, third set of clips (9)
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