4999 (not counting 1).
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The nearest number whose square ≤ 10000 is 100. Then the greatest odd number less that 100 is 99 so there are 50 odd numbers in the range 1- 99 inclusive whose squares are less than 10000.
200*50=10000
There are 20 odd numbers between 19 and 57
Their sum is 10000.
On the list of choices posted with the question, there is nothing that could be placed between two odd numbers.