In case you're curious about the previous method, here's how it would be done...

First define the following...

Array1:

=INT((ROW(INDIRECT("1:"&ROWS($A$16:$C$25)*COLUMNS($A$16:$C$25)))-1)/3)

Array2:

=MOD((ROW(INDIRECT("1:"&ROWS($A$16:$C$25)*COLUMNS($A$16:$C$25)))-1),3)

Array3:

=N(OFFSET($A$16:$C$25,Array1,Array2,1,1))

Then try...

=IF(SUM(IF(F16:F25<>"",IF(ISNA(MATCH("*"&F16:F25&"*",Array3&"",0)),1))),"Non-existing","Existing")

...confirmed with CONTROL+SHIFT+ENTER. If, however, the data contains both text and numerical values, the process of converting to a 1X30 array becomes much more expensive.

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