Difference between revisions of "2021 JMPSC Sprint Problems/Problem 11"
(→Solution) |
(→Solution 2 (General Method)) |
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Now apply <math>f(x)=x-2</math> to get | Now apply <math>f(x)=x-2</math> to get | ||
<cmath>S_2=\{1,2,3,\cdots,48\}</cmath> | <cmath>S_2=\{1,2,3,\cdots,48\}</cmath> | ||
− | Which clearly has cardinality <math>\boxed{ | + | Which clearly has cardinality <math>\boxed{48}</math>. |
~yofro | ~yofro |
Latest revision as of 18:55, 7 September 2021
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
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.