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Dr. Otter,
This is a manual solution: You can also use a macro - but that depends on how skilled you are.
I have assumed that your first blank column is H, and the data of interest is in columns F and G. IF that is not the case, then you need to adjust these instructions.
First off, make a copy of your sheet, and do this on the copy until you are sure you have done it correctly.
In H1, enter the formula
=F1
And copy to the right for 5 columns.
Then in H2, use the formula
=IF(F2="",F3,"")
and copy to I2.
In J2, use the formula
=IF(AND(F2="",F4<>""),F4,"")
and copy to K2.
In L2, use the formula
=IF(AND(F2="",F4<>"",F5<>""),F5,"")
and copy to M2.
Then copy H2:M2 down to match your rows of data. Finally, copy H:M and paste special values, and then delete columns F and G. Then select column B, use Ctrl-G choose the "Special..." button, select "Blanks" press "OK", right click the selection and choose Delete.... Entire row OK , and you are done.
If you ever have 4 rows of values for one ID, you need to use an extra 2 columns of formulas.
You can also use a macro - but that depends on how skilled you are.