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All multiples of 10 are exceptions to this condition. Reason :

$10^2 = 100$. On reversing 10 we get $01$. Now square it we get $01^2 = 1 = 01 = 001 = 0001 ..... and~so~on$. Now reversing it we get $10,100,1000 .....and~so~on$. So, the multiples of $10$ are exceptions. More clearly they will be in an undetermined form.

@Ram Mohith
–
You can twist the question in the direction of palindromes. Say you give examples for palindromes and ask whether it works all the time ( For other numbers too). And you give three options. Yes, always , No, never and Yes , sometimes. But do not make it too obvious

There is a question on this (but I forgot and cannot search). The real pattern is 1 followed by some number of 2's and when you reverse it still makes sense

Easy Math Editor

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## Comments

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TopNewest@Ram Mohith, There is a problem that goes something like this

$12^2= 144 ; 21^2 = 441$

$122^2 = 14884; 221^2 = 48841$

$1222^2 = 1493284; 2221^2 = 4932841$

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Yes. It is quite good.

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Try to find if there are any such numbers.

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Well I noticed that the 144 is 12 squared. And the prime factorization of 144 is 3^2 times 2^4 which is 4^2 and 3 and 4 are consecutive.

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AND THAT WAY WORKS

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Yes that is a good way finding such numbers. I too will try.

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P.S. I am 10 this my Brother's account

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You just take two consecutive numbers. Then multiply them. and then the rest works.

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My assumption WORKED. YAY

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I am thinking to frame a question based on these observations.

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May I assist

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Did you get still anymore numbers like these.

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I am trying to obtain a general form for these numbers or if there is some periodicity between the numbers .

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You cannot frame a question

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Why can't we ?

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It only works around 20

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All single digit integers will satisfy this condition the reason being when they are reversed the same number is obtained.

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True

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All multiples of 10 are exceptions to this condition. Reason :

$10^2 = 100$. On reversing 10 we get $01$. Now square it we get $01^2 = 1 = 01 = 001 = 0001 ..... and~so~on$. Now reversing it we get $10,100,1000 .....and~so~on$. So, the multiples of $10$ are exceptions. More clearly they will be in an undetermined form.

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Make sense

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This also works with $13$:

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My friend told me that on Friday but I forgot

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And if you take $14$ in base $20$ (so 24 in base 10) and square it, you get $18G_{20}$. If you square $42_{20}$ (81 in base 10) you get $G81_{20}$.

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Did you know that both the endings of 31 and 19 end in 61.

31 times 31 = 961

and

19 times 19 = 361

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Square 20. We get 400.

Reverse 20. We get 02.

Square 02. We get 004

Reverse 400. We get 004

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Good one again

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It only works below 20

EDIT: The pattern is with 1 and a followed number of 2'sLog in to reply

Ok. Should see about this !!!

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WAIT 10 and 11 work

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Sorry. It is around 20

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20 means squaring and reversing

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The idea of making a problem out of this out of question

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Unless it is a proof stating question

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Yes. Your point is also correct.

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But my idea is not to write a proof based question.

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Can you help me in my other notes

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surely.

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Lets go to interesting prime powers relationship(the name)

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There is a question on this (but I forgot and cannot search). The real pattern is 1 followed by some number of 2's and when you reverse it still makes sense

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