7
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I need to solve the pattern in given format

98     |    54     |   78
7641   |    3120   |   5402
714    |    494    |   726

43     |    56     |   02
4910   |    0298   |   7614
391    |    005    |   596

35     |    78     |   38
9081   |    4391   |   4602
234    |    823    |   ???

I have to find the last number with question mark.

Edit

Image source

enter image description here

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  • 4
    $\begingroup$ If you did not make this problem up, please provide a citation for the source. $\endgroup$ – Jeff Zeitlin Jan 29 '18 at 15:49
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    $\begingroup$ As in a school quiz? $\endgroup$ – Herb Wolfe Jan 29 '18 at 17:17
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    $\begingroup$ Is this strictly math? I ask because I don't want to go down a rabbit hole of discovering patterns within the numbers themselves only to find out later that the answer required knowledge of something completely different, like patterns in the periodic table or sports stats. $\endgroup$ – doggify Jan 31 '18 at 19:53
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    $\begingroup$ Mind if I ask what kind of class this was given in? I need to know how to approach the problem. How I've been doing it so far hasn't lead anywhere. $\endgroup$ – doggify Feb 1 '18 at 7:59
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    $\begingroup$ If it is unimportant than both middle values for 78 are shifted by 1. Maybe that's something important... :/ 5402 - 1 on each position is 4391. $\endgroup$ – Morfium Feb 5 '18 at 10:09
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+50
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My answer is

304.5671786568776109607614404480079620217332903018752941134...

Because

Those are clearly 3 by 3 matrices.
The determinants of the first two matrices are respectively -10154144 and 8656182, assuming those are aranged in an arithmetic sequence, we want the third one to be 27466508.
The determinant of the third matrix is (196389516 - 554633$x$) (here I replaced ??? by $x$ for readability reasons).
Solving for x gives the value 168923008/554633 which is roughly 304.5671786568776109607614404480079620217332903018752941134...

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  • $\begingroup$ I think it's not that easy $\endgroup$ – Doomenik Feb 7 '18 at 12:25
  • $\begingroup$ What do you consider to be the "first two matrices"? $\endgroup$ – Lolgast Feb 7 '18 at 12:25
  • $\begingroup$ I'm pretty sure it's not the answer either, but it's a pattern that completes the picture anyway, and as I thought it was pretty funny I decided to post it anyway, the matrices are the numbers written with a gray background in the question (doesn't look good in comments sorry) $\endgroup$ – Florian Bourse Feb 7 '18 at 12:29

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