2021 JMPSC Sprint Problems/Problem 11
Problem
How many numbers are in the finite sequence of consecutive perfect squares
Solution
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
.
~yofro
See also
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