BdMO National Junior 2008/7

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
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BdMO National Junior 2008/7

Unread post by samiul_samin » Sun Feb 24, 2019 9:15 am

A good number is the sum of a two digit number,with distinct digits,and its reverse.For example $37+73=110$ is good.How many good numbers are perfect squares?

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Junior 2008/7

Unread post by samiul_samin » Mon Feb 25, 2019 11:52 am

Answer:$\fbox 1$

Solution:
Suppose $d$ is a good number.
Then $d=10a+b+10b+a=11(a+b)$
So,$11|d$
As sum of the two, two-digit numbers is never greater than $198$,there is only $1$ good number and it is $121$.

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