Please help me with formulas to solve a 50 numbers problem

I think your sample sheet doesn't exactly match your description -- specifically, you said that you entered the numbers 1 to 20 in row 2, but you really only entered the numbers 1 to 19. That caused me some confusion at the beginning, but once I realized the mistake, I think I worked out something that will work for 19 or 21 or 20 numbers entered in row 2. Note that I am not a fan of big ugly megaformulas, so I used a block of helper cells on the way to getting the solution.

1) As I looked at the description and the sample sheet, it occurred to me that we are basically counting how many entries there are between row 2 and the row above the current row and subtracting that value from the count of the entries in the current row. =COUNT(A3)-COUNT(A$2:A2) entered in a convenient upper left corner of our helper block (I entered in A26). Note the mix of relative and absolute references, then copy down as far as needed (to row 37 in my case) and across as far as needed (column BR in my case). The result is a matrix of counts where 0s and negative numbers indicate that the number either hasn't been encountered yet or has been encountered more than once. A value of 1 indicates that this is the first time the number has been encountered, and should therefore be included in the count in column BS.
2) At this point, all that is needed is to count the 1s in each row. A simple COUNTIFS() works well for this =COUNTIFS(A26:BR26,1) copied down to BS37 (obviously, replace references to the location in the spreadsheet where you put the counting matrix).
3) To check the total, you can enter =SUM(BS26:BS37) where you want the check sum value to be.

Assuming I have understand the task correctly, something like that should work.

With your version of Excel, I had to add helper columns in BT:EK to make this possible - I couldn't think how to do it otherwise.

See attached.

WBD