To apply data validation without the drop downs use the following formula for custom data validation applied to the range B11:B31 on the 'Invoice' sheet:
Formula:
=OR(B11="",AND(COUNTIFS(PRODUCT!A$3:A$20,B11),COUNTIFS(B$11:B11,B11)=1))
This will allow the item number to be typed into one of the cells in the range B11:B31 on the 'Invoice' Sheet, as modeled in the attached file.
After looking at the layout a bit further it may be that you were actually wanting to type the item numbers into the 'Invoice Data' sheet.
If the latter is the case then the following formula would need to used as custom data validation and applied to column F on the 'Invoice Data' sheet:
Formula:
=OR(F1="",AND(COUNTIFS(PRODUCT!A$3:A$20,F1),COUNTIFS(F$1:F1,F1)=1))
Let us know if you have any questions.
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