Converting 3x10 array to a 1X30 array to run a Match formula

To tell you the truth I was trying to assist another user here: http://www.excelforum.com/excel-misc...-of-cells.html

and I had suggested a working formula as below:

=IF(SUM(IF(ISNA(MATCH("*"&$F$16:$F$25&"*",TEXT($A$16:$A$25,"########"),0)),IF(ISNA(MATCH("*"&$F$16:$F$25&"*",TEXT($B$16:$B$25,"########"),0)),IF(ISNA(MATCH("*"&$F$16:$F$25&"*",TEXT($C$16:$C$25,"########"),0)),1)))),"non existing","existing")

(which turns out isn't what they were looking for.. but got me thinking....)

I want to be able to shrink it to:

=IF(SUM(IF(ISNA(MATCH("*"&$F$16:$F$25&"*",TEXT($A$16:$C$25,"########"),0)),1)),"non existing","existing")

but I can't use the Red range... how could I consolidate the range to a single array?