Getting inspired too much!
Find the sum of all 2 digit numbers when flipped and added together result in a perfect square.
The answer is 484.
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1 solution
Same way! Answer is another perfect square :)
Exactly Same Way
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Do you remember, you reshare a similar problem?
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Yes I do, I did it on Tuesday.
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@Kushagra Sahni – Keep it up!!
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@Dev Sharma – Today is my NMTC Final exam. I am very nervous.
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@Kushagra Sahni – Best of luck. How can i participate?
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@Dev Sharma – You first need to clear stage 1 of it. To appear for stage-1 ask your school about it next year or maybe you will join a coaching institute so you can appear for it from there.
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@Kushagra Sahni – oh.. Tell me when would you be active on fb? Because moderators don't allow us to chat her
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@Dev Sharma – On Monday Afternoon write hi to me i will come
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@Kushagra Sahni – how was your exam? Share a note of all problems.
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@Dev Sharma – It was absolutely horrible .
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@Kushagra Sahni – I know you have got most problems correct. Please share a note about problems and your experience.
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@Dev Sharma – No seriously It was extremely difficult all intelligent kids in my batch also found it extremely tough. I will show you the questions tomorrow.
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@Kushagra Sahni – Thanks. I would WAIT
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@Dev Sharma – I will upload a note of all the questions by tomorrow
@Kushagra Sahni – hey ??????
Perfect solution.
Let the required two-digit number n = 1 0 a + b , where a , b = 1 , 2 , 3 , . . . 9 . Then, we have:
1 0 a + b + 1 0 b + a = 1 1 ( a + b ) = m 2 , where m is a positive integer. For 1 1 ( a + b ) to be a perfect square, a + b must be 1 1 . All the possible cases and their sum are as follows:
\[\begin{array} {} 29 &+ & 92& =& 121 \\ 38&+&83&=&121 \\ 47&+&74&=&121 \\ 56&+&65&=&121 \\ \hline &&&& \boxed{484} \end{array} \]