2021 JMPSC Sprint Problems/Problem 11
How many numbers are in the finite sequence of consecutive perfect squares
The perfect squares are from to . Therefore, the answer is the amount of positive integers between and , inclusive. This is just .
Solution 2 (General Method)
The set is Notice that the cardinality of is equal to the cardinality of For all functions with domain containing . In our case, apply to get Now apply to get Which clearly has cardinality .
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