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This sequence goes on forever, but here is the first 7 of them. The X's are just there to hide the actual digits. Can you find all the correct digits of the 8th entry?

1024, 90X1X, 25023X, 490364, X1031X0, XX1041X4, X690XXXX, ________?

Hint:

No complicated calculations needed. In fact, it's based on a very simple rule. I'm sure this sequence would've been solved within minutes if I didn't replaced the digits with X's.

More specific hint:

Squares involved

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  • $\begingroup$ Does the use of 'X' represent the sameness of all digits? $\endgroup$ – John Brookfields Jun 4 at 17:03
  • $\begingroup$ @JohnBrookfields No, it doesn't. $\endgroup$ – Prim3numbah Jun 4 at 17:06
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The pattern is

1024, 90X1X, 25023X, 490364, X1031X0, XX1041X4, X690XXXX
1024, 90216, 250236, 490364, 8103100, 12104144, 16904196

Hence, the next number is

22505256

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  • 5
    $\begingroup$ Why 05 in the middle vs. 04? $\endgroup$ – El-Guest Jun 4 at 17:08
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    $\begingroup$ Yes, that's also something that confused me. It seems like it increases every two numbers, but then 02 occurs thrice, so I'm not sure anymore. $\endgroup$ – sedrick Jun 4 at 17:10
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    $\begingroup$ @sedrick well done, but the mid number is incorrect. The mid numbers represents something else $\endgroup$ – Prim3numbah Jun 4 at 17:15
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The fist few digits represent the odd number squares and the last few digits represent the even number square. ($1^2$ and $2^2$, $3^2$and $4^2$ and so on.) So, the next number will be $22504256$. The numbers given are: $1024, 90216, 250236, 490364, 8103100, 12104144, 16904196$ and finally $22504256$

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  • $\begingroup$ Good work, but the mid number is not correct. Take a look on the comment section above $\endgroup$ – Prim3numbah Jun 4 at 17:26

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