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.

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 \( G81_{20} \).

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

@Ram Mohith
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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

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

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`\boxed{123}`

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

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It only works around 20

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You cannot frame a question

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Why can't we ?

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May I assist

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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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Did you get still anymore numbers like these.

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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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My assumption WORKED. YAY

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

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AND THAT WAY WORKS

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

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

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Try to find if there are any such numbers.

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Yes. It is quite good.

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This also works with \( 13 \):

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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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My friend told me that on Friday but I forgot

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

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Yes. Your point is also correct.

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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

Sorry. It is around 20

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20 means squaring and reversing

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Ok. Should see about this !!!

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WAIT 10 and 11 work

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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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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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