BdMO National Junior 2008/7
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- Posts:1007
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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?
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: BdMO National Junior 2008/7
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 $121$.
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 $121$.