# Difference between revisions of "2021 JMPSC Sprint Problems/Problem 11"

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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.