Want to make short a formula

Hi,

I have created a formula to find out last digit of 18 digit numbers. Actually I got this formula by using lugn algorithm. Here is the formula. Also attached a sample file in this regards.

Formula:

=IFERROR(A2&IF(VALUE(RIGHT(MID(A2,1,1)+IF(LEN(MID(A2,2,1)*2)=2,RIGHT(MID(A2,2,1)*2,1)+LEFT(MID(A2,2,1)*2,1),MID(A2,2,1)*2)+MID(A2,3,1)+IF(LEN(MID(A2,4,1)*2)=2,RIGHT(MID(A2,4,1)*2,1)+LEFT(MID(A2,4,1)*2,1),MID(A2,4,1)*2)+MID(A2,5,1)+IF(LEN(MID(A2,6,1)*2)=2,RIGHT(MID(A2,6,1)*2,1)+LEFT(MID(A2,6,1)*2,1),MID(A2,6,1)*2)+MID(A2,7,1)+IF(LEN(MID(A2,8,1)*2)=2,RIGHT(MID(A2,8,1)*2,1)+LEFT(MID(A2,8,1)*2,1),MID(A2,8,1)*2)+MID(A2,9,1)+IF(LEN(MID(A2,10,1)*2)=2,RIGHT(MID(A2,10,1)*2,1)+LEFT(MID(A2,10,1)*2,1),MID(A2,10,1)*2)+MID(A2,11,1)+IF(LEN(MID(A2,12,1)*2)=2,RIGHT(MID(A2,12,1)*2,1)+LEFT(MID(A2,12,1)*2,1),MID(A2,12,1)*2)+MID(A2,13,1)+IF(LEN(MID(A2,14,1)*2)=2,RIGHT(MID(A2,14,1)*2,1)+LEFT(MID(A2,14,1)*2,1),MID(A2,14,1)*2)+MID(A2,15,1)+IF(LEN(MID(A2,16,1)*2)=2,RIGHT(MID(A2,16,1)*2,1)+LEFT(MID(A2,16,1)*2,1),MID(A2,16,1)*2)+MID(A2,17,1)+IF(LEN(MID(A2,18,1)*2)=2,RIGHT(MID(A2,18,1)*2,1)+LEFT(MID(A2,18,1)*2,1),MID(A2,18,1)*2),1))=0,0,10-VALUE(RIGHT(MID(A2,1,1)+IF(LEN(MID(A2,2,1)*2)=2,RIGHT(MID(A2,2,1)*2,1)+LEFT(MID(A2,2,1)*2,1),MID(A2,2,1)*2)+MID(A2,3,1)+IF(LEN(MID(A2,4,1)*2)=2,RIGHT(MID(A2,4,1)*2,1)+LEFT(MID(A2,4,1)*2,1),MID(A2,4,1)*2)+MID(A2,5,1)+IF(LEN(MID(A2,6,1)*2)=2,RIGHT(MID(A2,6,1)*2,1)+LEFT(MID(A2,6,1)*2,1),MID(A2,6,1)*2)+MID(A2,7,1)+IF(LEN(MID(A2,8,1)*2)=2,RIGHT(MID(A2,8,1)*2,1)+LEFT(MID(A2,8,1)*2,1),MID(A2,8,1)*2)+MID(A2,9,1)+IF(LEN(MID(A2,10,1)*2)=2,RIGHT(MID(A2,10,1)*2,1)+LEFT(MID(A2,10,1)*2,1),MID(A2,10,1)*2)+MID(A2,11,1)+IF(LEN(MID(A2,12,1)*2)=2,RIGHT(MID(A2,12,1)*2,1)+LEFT(MID(A2,12,1)*2,1),MID(A2,12,1)*2)+MID(A2,13,1)+IF(LEN(MID(A2,14,1)*2)=2,RIGHT(MID(A2,14,1)*2,1)+LEFT(MID(A2,14,1)*2,1),MID(A2,14,1)*2)+MID(A2,15,1)+IF(LEN(MID(A2,16,1)*2)=2,RIGHT(MID(A2,16,1)*2,1)+LEFT(MID(A2,16,1)*2,1),MID(A2,16,1)*2)+MID(A2,17,1)+IF(LEN(MID(A2,18,1)*2)=2,RIGHT(MID(A2,18,1)*2,1)+LEFT(MID(A2,18,1)*2,1),MID(A2,18,1)*2),1))),"")

This formula is working fine. I need this formula in short. Please help me by doing this.

You explanation does not make sense, why would you need all that to get the last digit of an 18 digit number?

@davesexcel, I suspect the formula is taking apart the 18 digit number and depending on what numbers occur at different positions it is adding different numbers to the end - the 20 digit number (which BTW in the attached example is only 19 digits long).
It hurts my head to try to take it apart to see what each formula section is doing but I suspect that if Mofasol gave an explanation about what the criteria is for it to determine what number to append to the end something could be developed.

First time hearing about public digits organization. Very interesting issue. Now I can check if my social number is in right manner or not.

Try for A2 digits:

=A2&RIGHT(10-RIGHT(SUMPRODUCT(MID(A2,ROW($1:$9)*2-1,1)+MID(A2,ROW($1:$9)*2,1)*2-(MID(A2,ROW($1:$9)*2,1)+0>5)*9)))

with 9 = 18 digits/2. Change it to 8 for 16-digit case.

I got this
C2
=A2&MOD(SUMPRODUCT((MOD(MID(A2,ROW($A$1:$A$9)*2-{1,0},1)*{1,2}-1,9)+1)*(-MID(A2,ROW($A$1:$A$9)*2-{1,0},1)*{1,2}<0))*9,10)

and shorten one
=A2&MOD(SUMPRODUCT(MOD(MID(A2,ROW($1:$9)*2-{1,0},1)*{1,2},9)-(--MID(A2,ROW($1:$9)*2-{1,0},1)=9))*9,10)